That depends on the outside air temp (OAT)*. At OATs below 30°F, the heat pump is capable to heat the home, but the coefficient of performance might be 2.0 or less.

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...