Insulating exterior walls with no vapor barrier or sheathing...
my walls do not have any insulation, other than the bathroom (only because it got renovated this past Spring, and R-13 placed in the stud cavities), but the walls are air tight. At the coldest point last Winter, I did have to raise my thermostat to around 70, but normally keep it at 68. At night, normally 60, but had to raise to 62. This past month, since we have gotten the C/A, we keep the thermostat at 73 when home, and 76 when away, and cycles like it should.
It is about keeping the ceiling at the proper level for insulation (check your area on depth), and making sure that doors and windows are air tight. This year, we also placed Foil faced Foam board in the basement windows and sealed with caulk to stop air infiltration, and have noticed a big difference.
What do your bills look like between last year, and previous years, and how old is your HVAC system? These are also factors to consider, just like doors, windows, and insulation.