Verified answer

There is a drain tube on your heater box under the passengers side, If this becomes plugged or just gets kicked off, the heater box won't drain outside like it needs to. Also is the fluid on your floor coolant or just water? If it's coolant you may have a bad heater core. Check the connections where the heater hoses come into the heater core on the front of the firewall too. A leaking connection there can also pass into the heater box and run down on to the floor.Does your caliber have rear heating? There will be coolant hoses that run back to it too.

Dodge Caliber Water Leak Recall

I'd say it's either the A/C drain from the evaporator condensation or the heater core itself has sprung a leak and it'd cause the dampness just like you're experiencing as the heater core is just above the passenger feet area. Not an easy fix as the heater core has to be replaced which usually requires the dash be taken apart to access the heater core. Does the car seem to be using up coolant?

Does it happen in the rain? It may be bad caulking in the cowl (where the hood meets the windshield area). They had a recall on another dodge for that. But could also be heater core or ac evap drain.