Usually electric heat is more inefficient than gas. I would have someone check your attic insulation to see if it is sufficient, as well as seal any drafts in your home.
It's freezing cuz it's 65. Mine is a warm 74 but my bills aren't 100 either but i refuse to be cold. 65 is way too cold for me. My electric heater only upped my electric bill by 15 dollars.