It's yet another challenge for the bipartisan coalition striving to pass a comprehensive immigration reform bill.
A key procedural vote is set for today that could clear the way for a final vote on the bill.
The coalition cleared a major hurdle yesterday by defeating a proposal offered by California Senator Dianne Feinstein.
It would have allowed the estimated 12 (m) million illegal immigrants to remain in the US and eventually become citizens.
Several lawmakers who voted against it said they didn't want to, but did so to ensure the survival of the broader bill.
It allows two-thirds of the illegal immigrants to stay, but makes the other third leave.
The Senate could approve the bill later today or tomorrow, setting up tough negotiations with the House to reach a compromise.