Engine misfires at cruise speed 54-55 mph - 2000 Mercury Grand Marquis

Not the speed sensor , misfire ? plug , plug wire etc..... Check engine light on ? Have diagnostic's done on the vehicle ,check misfire counters on mode 6 . Do you know what this is ? If not your best bet ,take it to a qualified repair shop.

You can try a drive cycle, see if it helps? There may be an idle relearn, if just idle issue? Usually it will relearn idle on its own by driving.
Drive Cycle Recommendations:

1. Most OBDII monitors will complete more readily using a "steady foot" driving style during cruise or acceleration modes. Operating the throttle in a "smooth" fashion will minimize the time required for monitor completion.
2. Fuel tank level should be between 1/2 and 3/4 fill with 3/4 fill being the most desirable.
3. The Evaporative Monitor can only operate during the first 30 minutes of engine operation. When executing the procedure for this monitor, stay in part throttle mode and drive in a smooth fashion to minimize "fuel slosh".

WARNING
STRICT OBSERVANCE OF POSTED SPEED LIMITS AND ATTENTION TO DRIVING CONDITIONS ARE MANDATORY WHEN PROCEEDING THROUGH THE FOLLOWING DRIVE CYCLES.
For best results, follow each of the following steps as accurately as possible:
OBDII Monitor
Exercised Drive Cycle Procedure
Purpose of
Drive Cycle Procedure Drive Cycle
Preparation 1. Install scan tool. Turn key on with the engine off. Cycle key off, then on. Select appropriate Vehicle & Engine qualifier. Clear all DTC's/ Perform a PCM Reset. Bypasses engine soak timer. Resets OBDII Monitor status. 2. Begin to monitor the following PIDs: ECT, EVAPDC, FLI (if available) and TP MODE.
Start vehicle WITHOUT returning to Key Off. 3. Idle vehicle for 15 seconds. Drive at 64 Km/h (40 MPH) until ECT is at least 76.7°C (170° F). Prep for Monitor Entry 4. Is IAT within 4.4 to 37.8°C (40 to 100° F)? If Not, complete the following steps but, note that step 14 will be required to "bypass " the Evap monitor and clear the P1000. Engine warm-up and provide IAT input to the PCM. HEGO 5. Cruise at 64 Km/h (40 MPH) for up to 4 minutes. Executes the HEGO monitor. EVAP 6. Cruise at 72 to 104 Km/h (45 to 65 MPH) for 10 minutes (avoid sharp turns and hills) Note, to initiate the monitor: TP MODE should =PT, EVAPDC must be >75%, and FLI must be between 15 and 85% Executes the EVAP Monitor (If IAT is within 4.4 to 37.8° (40 to 100°F)) Catalyst 7. Drive in stop and go traffic conditions. Include five different constant cruise speeds, ranging from 40 to 72 Km/h (25 to 45 MPH) over a 10 minute period. Executes the Catalyst Monitor. EGR 8. From a stop, accelerate to 72 Km/h (45 MPH) at 1/2 to 3/4 throttle. Repeat 3 times. Executes the EGR Monitor. SEC AIR/CCM (Engine) 9. Bring the vehicle to a stop. Idle with transmission in drive (neutral for M/T) for 2 minutes. Executes the ISC portion of the CCM. CCM (Trans) 10. For M/T, accelerate from 0 to 80 Km/h (o to 50 MPH), continue to step 11. For A/T, from a stop and in overdrive, moderately accelerate to 80 Km/h (50 MPH) and cruise for at least 15 seconds. Stop vehicle and repeat without overdrive to 64 Km/h (40 MPH) cruising for at least 30 seconds. While at 64 Km/h (40 MPH) , activate overdrive and accelerate to 80 Km/h (50 MPH) and cruise for at least 15 seconds. Stop for at least 20 seconds and repeat step 10 five times. Executes the transmission portion of the CCM. Misfire & Fuel Monitors 11. From a stop, accelerate to 104 Km/h (65 MPH). Decelerate at closed throttle until 64 Km/h (40 MPH) (no brakes). Repeat this 3 times. Allows learning for the misfire monitor. Readiness Check 12. Access the ON-Board System Readiness (OBDII monitor status) function on the scan tool. Determine whether all non-continuous monitors have completed. If not, go to step 13. Determines if any monitor has not completed. Pending Code Check and Evap Monitor "Bypass" Check 13. With the scan tool, check for pending codes. Conduct normal repair procedures for any pending code concern. Otherwise, rerun any incomplete monitor.
Note: if the EVAP monitor is not complete AND IAT was out of the 4.4 to 37.8° C (40 to 100° F) temperature range in step #4, or the altitude is over 2438 m. (8000 ft.), the Evap "bypass" procedure must be followed.Proceed to step 14. Determines if a pending code is preventing the clearing of P1000. Evap Monitor "Bypass" 14. Park vehicle for a minimum of 8 hours. Repeat steps 2 through 12. DO NOT REPEAT STEP 1. Allow the "bypass" counter to increment to two.
© Ford Motor Company

It is HVAC 1fuse #39 in the rear fuse block ,this powers the on/off switch for cruise control ! Fuse Block - Rear Beneath the left rear seat. What engine does it have ? 4.2 L or 5.3 l There is no vacuum involved in the operation of the cruise control ! Your vehicle has electronic throttle control .
Cruise control is a speed control system that maintains a desired vehicle speed under normal driving conditions at vehicle speeds above 40 km/h (25 mph). Steep grades may cause variations in the selected vehicle speeds.
The following are the main components of the Cruise Control System:
?€¢
The powertrain control module (PCM)

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The On/Off switch

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The Resume/Accel switch

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The Set/Coast switch

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The TCC brake switch

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The stop lamp switch

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The throttle actuator control (TAC) motor

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The vehicle speed sensor

Cruise Control Engaged
The cruise control system will engage and adjust the vehicle speed based on the activation of the following cruise control switches:
?€¢
On/Off

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Resume/Accel.

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Set/Coast

The cruise control switches are located on the multifunction/turn signal lever.
The powertrain control module (PCM) monitors the signal circuits of the cruise control switches in order to determine when to capture and maintain the selected vehicle speed. The PCM uses the throttle actuator control (TAC) module motor in order to control the vehicle speed. For further information on the TAC System, refer to Throttle Actuator Control (TAC) System Description in Engine Controls - 4.2 L.
Ignition positive voltage is supplied from the 10 ampere HVAC 1 fuse to the cruise control switch via the ignition 3 voltage circuit. When the normally open cruise control On/Off switch is turned On, the switch closes and the PCM detects a high signal voltage on the cruise control on switch signal circuit. When the normally open Set/Coast switch is pressed, the switch closes and the PCM detects a high signal voltage on the cruise control set/coast switch signal circuit. To engage the cruise control system, turn the On/Off switch On and momentarily press the Set/Coast switch. The PCM will confirm that the cruise control enable criteria has been achieved. The PCM will engage the cruise control system and record the selected vehicle speed. The PCM sends a class 2 message to the instrument panel cluster in order to illuminate the cruise control indicator. Pressing the accelerator pedal, while the cruise control system is engaged, will allow the driver to override the cruise control system in order to accelerate the vehicle beyond the current set vehicle speed. When the accelerator pedal is released, the vehicle will decelerate and resume the current set vehicle speed. The driver can also override the current set vehicle speed via the Set/Coast switch and the Resume/Accel switch. When the cruise control system is engaged, pressing and holding the Set/Coast switch will allow the vehicle to decelerate from the current set vehicle speed without deactivating the cruise control system. When the Set/Coast switch is released, the PCM will record the vehicle speed and maintain the vehicle speed as the new set vehicle speed. When the cruise control system is engaged, momentarily pressing the Set/Coast switch will allow the vehicle to decelerate at 1.6 km/h (1 mph) increments for each time that the Set/Coast is momentarily pressed, with a minimum vehicle speed of 37 km/h (23 mph). When the normally open Resume/Accel switch is activated, the switch closes and the PCM detects a high signal voltage on the cruise control resume/accel switch signal circuit. Activating and holding the Resume/Accel switch, when the cruise control system is engaged, will allow the vehicle to accelerate to a greater vehicle speed than the current set vehicle speed. When the Resume/Accel switch is released, the PCM will record the vehicle speed and maintain the vehicle speed as the new set vehicle speed. When the cruise control system is engaged, momentarily activating the Resume/Accel switch will allow the vehicle to accelerate at 1.6 km/h (1 mph) increments for each time that the Resume/Accel switch is momentarily activated, with the maximum acceleration total of 16 km/h (10 mph) over the current set vehicle speed . Momentarily activating the Resume/Accel switch, after the cruise control system has been disengaged by pressing the brake pedal, will recall the previous set vehicle speed that is recorded in the PCM.

make a mixture 1 liter two table spoon of salt in bottle with spray
engine idle spray your mixture not too much and see if you have spark on wire ,coil you won't see it if too much mixture
and about spark plugs you could change it too
you have a misfire

Since the transmission shifting and torque converter lock (cruise speeds) up are computer controlled you need to have a scanner hooked up that can read Transmission control module (TCM) fault codes. Also check for engine codes as this could be a misfire, but in that case the check engine light should be flashing while the engine is misfiring and set a fault code. If no codes of any kind are present in memory when the testing is done you almost certainly have a mechanical fault in the transmission like a malfunctioning torque converter clutch, but even that should set a fault code, so have the testing done.

Here is the OBD2 emission system drive cycle test procedure.
Engine coolant temp must be below 70c (158f) before starting the engine for either the first or second trip
The fuel level should be less than 1/2 full
First trip:
Start engine, idle for at least 1.5 minutes
Drive 3 minutes, hold b/f schdl: 1.5-2.0 msec, selector lever "3rd" eng rpm 1,800-2,000 A/C switch:ON Hold the recommended b/f schdl range. Allow road speed to vary as necessary.
Drive at 55-65 mph for 1.5 min b/f schdl 2.0-3.2 msec, selector lever "5th" Engine rpm 2,200-3,000
IGN "off" for at least 10 seconds (not more than 5 min)
Dive at 50-60 mph for 3 minutes Selector lever "4th" keep engine speed above 3,000 rpm Allow speed to vary if necessary. Do not decelerate for more than 3 consecutive seconds. A/C switch ON.
Drive at a steady state cruise of 53-58mhp b/f schdl more than 1.8 msec selector lever "5th" eng rpm 2,400-2,600
Downshift to "4th" and decel more than 5 seconds without breaking, then idle for 1 minute.
Drive two minutes b/f schdl less than 2.0 msec Accelerate to 41 mph, decelerate to 34 mph, accelerate to 41mph. Do not completely release the accelerator. A/C switch off.
Idle 1 minute in park or neutral
Drive two minutes Steady state cruise at 31-44 mph. Selector lever "4th" A/C switch OFF. Hold the accelerator pedal as steady as possible. Allow speed to change if necessary.
End of first trip. Turn the key off the begin the second trip.
Second trip:
Start engine, idle for at least 1.5 minutes
Drive 3 minutes, hold b/f schdl: 1.5-2.0 msec, selector lever "3rd" eng rpm 1,800-2,000 A/C switch:ON Hold the recommended b/f schdl range. Allow road speed to vary as necessary.
Drive at 55-65 mph for 1.5 min b/f schdl 2.0-3.2 msec, selector lever "5th" Engine rpm 2,200-3,000
IGN "off" add four gallons of fuel
Dive at 50-60 mph for 3 minutes Selector lever "4th" keep engine speed above 3,000 rpm Allow speed to vary if necessary. Do not decelerate for more than 3 consecutive seconds. A/C switch ON.
Drive at a steady state cruise of 53-58mhp b/f schdl more than 1.8 msec selector lever "5th" eng rpm 2,400-2,600
Downshift to "4th" and decel more than 5 seconds without breaking, then idle for 1 minute.
Drive two minutes b/f schdl less than 2.0 msec Accelerate to 41 mph, decelerate to 34 mph, accelerate to 41mph. Do not completely release the accelerator. A/C switch off.
Idle 1 minute in park or neutral
Drive two minutes Steady state cruise at 31-44 mph. Selector lever "4th" A/C switch OFF. Hold the accelerator pedal as steady as possible. Allow speed to change if necessary. I especially like the part where they want you to add four gallons of fuel. Not three gallons, not five gallons, four gallons. Gotta love those Nissan engineers. ...and of course they state that if the trace is not followed exactly (i.e. you botch the acceleration/deceleration) you have to start all over again from scratch

First I'll assume you haven't read the owners Manuel, Cruise control is not perfect on any vehicle. if coming to a hill put foot on gas to help rpm, going down hill put foot on brake to keep same speed, cruise control operates off of engine vacuum. Speed sensors can be affected by putting on smaller or bigger tires than what is on drivers door.

Your cruise is not desinged to work at those low speeds. The cruise module needs vacum that your engine cannot produce at those low rpm's. Most will not work under 35-45 mph.

Check for a engine misfire corroded plug wire ends or coil tower,cracked spark plug,bad plug wire.

IMHO, I think that the broken cable is what is causing the problems. It "confuses" the programing of the CPU or computer.