For a fossil fuel plant that might convert fuel to electricity with ~35-40% efficiency, a heat pump with a CoP of 2.0 will be less efficient overall than a 90% gas furnace.
* More precisely, on the spread between the OAT and the indoor temp, but since the latter is basically a fixed figure...
1 kWh of electricity run thru a resistive heater will generate 3412 BTU
1 Ccf of gas contains the equivalent energy as 29 kWh, but will only generate 8.7 kWh when run thru thermal generation (assuming 40% efficiency and 10% transmission losses).
If you're just trying to make heat, directly burning the gas will consume much less energy - and make fewer emissions - than gas > electricity > heatpump > heat.
In the end, the HP will be up to 30% more efficient than strip heat (in my case the crossover point is under 10f where strip heat is cheaper to operate).
I built a breakdown chart showing cost per kWh for both heat pump and strip heat, then added gas to it as a comparison.