Without being there to look at everything, it's impossible to say.
If yours is a multi-stage furnace, it may be running at low levels much of the time just to hold your set temperature. However, when your setback program says it should be permitting the house to drop to 60, it shouldn't be on at all. If you have the fan set to ON that's one thing but the burner should shut down entirely.
Just so you know, anyone that comes along and tells you to get rid of the programmable thermostat "because it takes more energy to get back to the set temperature than it does just to hold it there" is wrong. Disregard them. I doubt if I need to tell you that, since you already had the good sense to both install one and give it a good setback. But I'm including it so other people will see it too.
Come back with more information. We need the full model number of the HVAC (particularly the furnace) and the thermostat, and preferably a photograph of the wiring at the furnace fan control board, and the wiring connections inside the thermostat. With that info we may be able to help more.