The amendment, from Rep. Diane BlackDiane Lynn BlackThe Hill Interview: Budget Chair Black sticks around for now House to vote on budget next week Blackburn says she's interested in Corker's seat MORE (R-Tenn.), is a GOP response to the Obama administration's suit against Arizona's immigration law. That law requires local law enforcement officers to determine whether people are legal U.S. residents if they are stopped for other reasons.

Democrats say state laws such as Arizona's intrude on the federal government's responsibility to enforce immigration laws. But Republicans have said these and other laws are needed because the federal government has failed to enforce federal law, and that illegal immigrants are entering the United States, committing crimes and otherwise taking up federal and state resources.

— This story was updated at 10:47 p.m. to reflect the later request for a recorded vote, and again at 12:15 a.m. Wednesday to reflect the roll-call vote.