My question is this: do you have an abundant supply of free natural gas?
If so, it is economical at any efficiency. At some low temperature, you would not move enough BTU's with the heat pump to keep up with the thermal losses of the home. You could then rev up your engine and harvest the additional heat generated.
If not, most individuals in the field switch from air-source heat pumps to straight gas furnaces at a balance point somewhere around 20 degF due to the shortcomings of the heat pump system. It is just not wise to run the heat pump constantly at low COP when you can cycle a gas boiler or furnace to provide the same heat.
Above this balance point (most of the time in the USA), a heat pump makes sense, regardless of how you power it.
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