Not really - the U.S. (except Montana) makes work at-will, where either side can terminate the work immediately without cause (although it can't be for reasons discriminatory of a protected class like race, religion, etc). You might be able to get damages for misrepresentation at most, but you'd have to show they never intended to hire you in the first place, or perhaps on the basis they allegedly didn't clarify that the offer is contingent on a background check.