My furnace turns off while the thermostat said it is on. I have to turn the thermostat off and on again to get the furnace to come back on. Is it the thermostat?

Does it fire up for a short time and shut off?

Not likely a stat problem. Going to have to go to the furnace and watch to see what is happening when it fails. Could be as simple as a dirty flame sensor, or plugged condensate drain line or trap, or could be much more involved. Without being there to see the unit fail, Im afraid we can't be of much help. Make and model of unit may help us, and if it has a diagnostic light, knowing what code it is blinking when the unit fails would also help.