Our air conditioner unit outside turns on but the furnace blower will not. It worked fine until about 2 days ago.

Try setting the thermostat blower switch from auto to ON then post back with the results.

It still won't turn on.

If the blower will still not run then you will need to check the blower relay,blower motor capacitor or the blower motor itself. One of these items has to be defective. And while you are checking make sure the thermostat is activating the green low voltage blower control wire.