My MIL [malfunction indicator light] came on while I was driving and it stays on. COuld it be the exhaust system or the engine????

when you turn on your ignition to the point before engaging the starter all your warning lights should light up. The Engine Check Light is very obvious, except they throw convention to the wind and show it as 'Service Engine Soon' lamp 'Malfunction indicator lamp (MIL)'.
Page 63 - Section 2-7 Instruments and controls

Malfunction indicator lamp (MIL) If this indicator lamp comes on steady or blinks while the engine is running, it may indicate a potential emission control malfunction. The malfunction indicator lamp may also come on steady if the fuel filler cap is loose or missing, or if the vehicle runs out of fuel. Check to make sure the fuel filler cap is installed and closed tightly, and that the vehicle has at least three gallons of fuel in the fuel tank. After a few driving trips, the lamp should turn off if no other potential emission control system malfunction exists.

http://www.vadennissanservicecontracts.com/owners-manual/nissan/2001-Nissan-Frontier.pdf

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How does the vehicle run ?
Malfunction Indicator Lamp (MIL) Always On
Circuit Description
Ignition voltage is supplied to the malfunction indicator lamp (MIL). The powertrain control module (PCM) turns the MIL ON by grounding the MIL control circuit.
MIL Operation
The MIL is located on the instrument panel (IPC).
MIL Function ?€¢
The MIL informs the driver that a malfunction has occurred and the vehicle should be taken in for service as soon as possible.

?€¢
The MIL illuminates during a bulb test and a system test.

?€¢
A DTC will be stored if a MIL is requested by the diagnostic.

You could have a bad instrument cluster ! Here is part of diagnostic flow chart for your vehicle !

1

Did you perform the Diagnostic System Check-Engine Controls?
Go to Step 2
Go to Diagnostic System Check - Engine Controls

2

1. Turn OFF the ignition.
2. Disconnect the PCM.
3. Turn ON the ignition, with the engine OFF.
4. Observe the MIL.

Is the MIL illuminated?
Go to Step 3
Go to Step 5

3

1. Remove the instrument panel cluster (IPC). Refer to Instrument Cluster Replacement in Instrument Panel, Gages, and Console.
2. Test the MIL control circuit for a short to ground. Refer to Circuit Testing and Wiring Repairs in Wiring Systems.

Did you find and correct the condition?
Go to Step 6
Go to Step 4

4

Replace the IPC. Refer to Instrument Cluster Replacement in Instrument Panel, Gages, and Console.
Did you complete the replacement?
Go to Step 6

5

Replace the PCM. Refer to Powertrain Control Module Replacement .
Did you complete the replacement?
Go to Step 6

see this chart troubleshooting and fix it.
God bless you
Check Engine or
Malfunction indicator light (MIL)
The Check Engine or Service Engine Soon light or an icon resembling the engine is called, in technical terms, the Malfunction Indicator Light or MIL. The MIL light comes on when your vehicle's computer detects a fault that can affect your vehicle's fuel economy and emissions. There is no button to reset the Check Engine light, but if the fault that caused it doesn't happen again, the light will turn off by itself. If the MIL light stays on, have the problem checked out, because in some cases, the problem could get worse if not repaired in time. Think of the Check Engine light as an early warning sign. To check why your MIL light came on, your dealer or mechanic will have to diagnose your car with a special scan tool.

Check for codes then google them, to see what
vehicle system failed

Check lights have been on all vehicles for 32 years,
long time not be up to speed

Check out OBD2 Systems when your on Google

I wouldn't drive it, if the light is flashing, other than to a repair
shop

Flashing MIL Lamp on some vehicles is a Class A cylinder
misfire & can ruin the exhaust converter & other things

When you have any light stay on your dash after the motor
is running, you got a problem

Whenever this warning light or any other stays on in the dash it is indicating that the systems control module (or the system sensor in the case of lights like low oil pressure, door open indicators etc.) has detected a fault, it then disables the system (this applies to ABS,TCS, TCM, SRS, TPMS, MIL, CEL and BCM faults and others) as long as the light is on. You must now have the dealer hook up a special electronic diagnostic tool and "scan" the system for the fault code that is stored for the problem(s)

Legend of Abbreviations. ABS Anti-lock brake system. TCS Traction control system, TCM Transmission control module, SRS Supplemental restraint system, BCM Body control module. TPMS Tire Pressure Monitor System, MIL Malfunction Indicator Lamp, CEL Check Engine Light.

When a 'check engine light' (MIL=Malfunction Indicator Lamp) is turned on, there is a DTC (Diagnostic Trouble Code) set/stored in the ECM/PCM (Engine Control Module/Powertrain Control Module). This code identifies which engine management system component/function experienced a malfunction. Once you pull/read this code, you may begin diagnosis.

A malfunction indicator lamp (MIL), commonly referred to as the "Check Engine Light" is an indicator of malfunction of the computerized engine management system. It is found on the instrument console of most automobiles. When illuminated, it is typically either an amber or red color. On vehicles equipped with OBD-II, the light has two stages: steady (indicating a minor fault such as a loose gas cap or failing oxygen sensor) and flashing (indicating a severe fault, that will eventually destroy the catalytic converter, such as a misfire). When the MIL is lit, the engine control unit stores a fault code related to the malfunction, which can be retrieved with a scan tool and used for further diagnosis. The malfunction indicator lamp is usually labeled with the text check engine, service engine soon, check engine soon, or a picture of an engine.
The MIL appeared in the early 80s along with computerized engine controls. Even the earliest systems, such as GM's CCC (Computer Command Carburetor) system had self diagnosis functionality. When the computer detected a fault, it illuminated the MIL. Up until OBDII, on most cars the MIL could output codes, when two pins on the ALDL are jumped, the light would flash the codes, for instance (blink) (pause) (blink) (blink) for code 12. Some manufacturers retained this feature even after OBDII, such as Honda.

Hope this help (remember comment and rated this). Good luck.

Probably a bad COIL-PACK

P0650 Malfunction Indicator Lamp (MIL) Control Circuit Malfunction

Malfunction Indicator Lamp (MIL) is located on the instrument panel. When the ignition switch is turned ON without engine running, MIL will light up. This is a bulb check. When the engine is started, MIL should go off. If MIL remains on, the on board diagnostic system has detected an engine system malfunction.

Possible Causes:

Harness or connectors (MIL circuit is open or shorted.)

MIL bulb may be faulty

I had the samething happen to my Jetta. I took it to the dealer and nothing was wrong.
I would think it's safe to drive until Monday when the VW shop opens.
My 2 cents