First class price, economy seat?

Anyone know what happens if you buy a first class ticket for an airline, but
they have no first class seats available?

After a royal ****up by the tools at Flight Centre, I'm trying to re-book a
trip between Vegas and Mexico and there's only first class tickets (and
prices!) left. Problem is their seating plan shows no seats available onm
one of the two legs and says "a seat will be assigned at check in".

I don't want to pay top dollar for an economy seat. Am I better off finding
another flight, or wil they (US airways) pull something out of a hat?

Thanks,
]v[