I gave a 30 day notice but the home I was going to rent fell through. Now my current property manager is saying I still have to get out because they have applicants for the house. No one has even seen it (including the property manager) and I have no where to go. I asked if I could stay and of course pay rent but they are adamant I move. Do I have any leg to stand on?

NO, they have all the cards.

You could apply too, but it appears that they don't want you for some reason.

Did you have a lease? What does the lease say?

A few US states have laws about changing one's mind and wanting to stay. But you would have to be a tenant in good standing.