I decided to go out and buy a new thermostat because the old one was having issues with being on auto. I would set it on 72, but it would rarely come on and the inside temp would stay around 60 unless I turned the fan to On. Anyway, so I went out and bought a nice programmable thermostat and installed it. It is still doing the same thing! I don't get it! I came home and it was 60 in the house when I have it set to 72. I've had to turn the fan to on just so it'll warm up. Does anyone know what the issue might be?

Seems to be a pre-existing wiring condition that is incorrect, and would not be corrected with a new t'stat. This may be at the stat, however I believe it is how it is connected at the furnace, and may be beyond your capabilities. The wires need to be identified and traced at the stat and the furnace.

Usually a red comes from a transformer to R on the stat, a white at the stat is on W and goes back to the furnace to start the furnace burner, and a third wire at the stat is on G terminal goes back to a relay that brings the fan on, manually.

At the furnace , the wire W that starts the furnace burner, the burner relay or some other sensor is waiting for heat in the furnace to rise, and closes to switch power on to the fan, automatically. This is where I believe your real problem lies.

Can you get back with more details of wires, colors, and how they are connected? Perhaps some photos to help us see what you have and maybe help you correct the problem.

Well it only had 4 wires. White, Red, Green, and Blue. The blue wire was connected to the Y spot on the old thermostat. I haven't looked at the furnace yet, but I will go peak at it once I get home.

OK since you only mentioned heat, and did not mention AC, I did not mention the blue wire, which is for the AC compressor, and should be connected to the Y terminal on the stat. There is not much that can be done incorrectly at the stat, therefore the problem does lie at the furnace controls.