But House Majority Leader Eric CantorEric Ivan CantorEric Cantor: Moore ‘deserves to lose’ If we want to make immigration great again, let's make it bipartisan Top Lobbyists 2017: Hired Guns MORE (R-Va.) stripped the rules from the bill, arguing the provisions were too broad and could have unintended or contradictory consequences. The White House said at the time that it did not support Cantor's move to do so.

Still, Senate leaders decided to move ahead with the House version of the bill rather than continue to squabble over the provisions, voting 96-3 Thursday to advance the legislation to Obama's desk.

“This represents Congress at its best,” Sen. Joe Lieberman (I-Conn.) told reporters Thursday. “We dealt with it quickly and on a bipartisan basis ... hopefully this will be a model for other critical legislation that we ought to be adopting.”

Cantor also released a statement hailing the bipartisan cooperation on the legislation.

“The STOCK Act is a product of bipartisan efforts in the House and the Senate and will help restore the public’s trust in their elected officials,” Cantor said.