“I actually think it’s more likely, if we take the Senate, that we will have immigration reform,” said Rep. Raul Labrador. “We will be able to do it on a step-by-step approach like most Republicans have been asking to do and I think the American people want.”

Labrador, who was a member of the bipartisan House group working on the issue before exiting, foresees a Republican-controlled Congress passing a series of bills that deal with the border and focus on interior security and guest-worker programs.

“I don’t want to mislead; it’s a difficult lift as we all know,” Rep. Mario Diaz-Balart told BuzzFeed News. “But we would have a better shot at getting it done if Republicans take control of the Senate for the simple reason that it could be initiated in the House with close coordination with the Senate.”

Actual Republican-passed immigration legislation could put President Obama in a very difficult political position: Sign bills that don’t accomplish all of what Democrats want, or accept smaller, incremental changes to U.S. immigration policy.