No heat pump will put out much, if any at 6 degrees.
A heat pump is an air conditioner that reverses cycle via a reversing valve that re directs the refrigerant flow in the unit, in ac mode,
heat from indoors is rejected outdoors in the heat mode the heat from outdoors is rejected indoors.
The system does this by evaporating and condensing refrigerant.
For the refrigerant to be "boiled" or "change state" from a liquid to a vapor a temperature differential must exist, meaning the heat from the outdoor air must "boil" the liquid refrigerant.
For this to be possible the liquid refrigerant must be colder than the 6 degrees ambient or it will not boil anything.
For a refrigerant used for AC to be that cold the pressure will be in a vacuum for most refrigerants temperature pressure relationship.
Heat pumps below 40 degrees ambient outdoor temperature are
not effective, at this temperature outside drops a degree lower it further degrades the heat output .Power companies that finance Heat pumps typically will install an outdoor thermostat to prohibit the 2nd stage or electric heat strips from coming on until it is 40 or below outdoors, at a certain point well before 6 degrees a heat pump should be ran on the emergency heat mode which is the heat strips and the fan. Since 1500 Watt electric heaters are available at Wal-Mart for $20 the best alternative in this situation would be to buy a few of them.