Why,when I set my thermostat at 72 the furnace won't heat past 66-68.

Could be the thermostat
Could be the furnace
Try disconnecting the R and W wires at the furnace and using a wire jumper the R and W connections. If after doing that the furnace heats the house past the 66-68 degree lever you have a thermostat problem if not and the furnace will not heat past the 66-68 level then you have a furnace problem.

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Originally Posted by hvac1000

Could be the thermostat
Could be the furnace
Try disconnecting the R and W wires at the furnace and using a wire jumper the R and W connections. If after doing that the furnace heats the house past the 66-68 degree lever you have a thermostat problem if not and the furnace will not heat past the 66-68 level then you have a furnace problem.

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I just installed a new thermostat.What may be the furnace problem

What's your filter look like?

Did you do all the settings correctly if it is a new digital thermostat?
As mentioned by MarkwithaK a dirty air filter,dirty A/C evaporator coil, or closed registers/restricted return airs will have a big effect on proper furnace operation.
Naturally an improperly operating furnace with out of range sensors and other defective controls can also cause this kind of problem.