GOP lawmakers say that with Republicans in charge of both chambers, leadership in the House would have a negotiating partner across the Capitol they could trust.

Republicans also would have more leverage with President Obama in negotiating a bill to secure the border and deal with the estimated 11 million undocumented immigrants already in the United States.

“With the caveat that it’s a very difficult issue, I think the likelihood is better if Republicans take the Senate,” said Rep. Mario Diaz-Balart (R-Fla.), a leading GOP voice for immigration reform.

“I think there would certainly be greater trust between the House and Senate in agreeing on something,” said Rep. Jeff Denham (R-Calif.), who like Diaz-Balart supports providing a path to citizenship for illegal immigrants. “This is an American issue. So I expect this party to come together on it. And I’m going to continue driving it.”