My fiances 2008 chevy cobalt is leaking a lot of water under the glove compartment and it is soaking the carpet/ floors, what can we do to fix this terrible problem?

Couple quick questions.... Does it have a sunroof? Has the windshield ever been replaced? Do you get any water drops from the AC vents when it is on high? Three things can be going on. A sunroof drain is clogged, causing the water to drain down the a-pillar and into the carpet. The Ac evaporator box drain is clogged, causing water to pool up in the evap box and overflow onto the carpet. You can also have a leak at the windshield that can be a result from an improper replacement at some point of the windshield. Check those three things and see where you stand.

I would pressur check the collant system Sounds like heater core to me

You say it is water, so that would rule out the cooling system, unless by water you mean liquid. In that case it is important to first determine if this liquid is coolant or just plain water. Then refer to the advice of the above two posters.