Have a Heil high efficiency furnace which works fine with heat and ac, but the fan will not go when thermostat is set to the on position and heat/air are off... is the a furnace problem or a thermostat problem??

It could be a low voltage wiring problem or thermostat problem. Since the blower comes on OK in the heat and cool mode the problem is the signal from the thermostat G terminal to the indoor unit. When you place the thermostat fan mode in ON the G wire sends a signal to the indoor unit to turn the fan on. Check the wiring first then if OK it is probably the thermostat.