Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) has all but ruled out the Senate making a second attempt at immigration reform legislation this year.

"Honestly ... I can't see us going back to immigration this year unless there was some proposal that the president actually was OK with and said he was willing to sign. I don't think he's OK with anything that I've seen coming our way," McConnell told Fox News.

He added that the "short answer" is it's "not on the agenda in the Senate."

ADVERTISEMENT

McConnell's comments come as House Republicans are barreling toward a make-or-break moment in their immigration reform fight. House Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) is expected to pitch a compromise to rank-and-file members during a closed-door caucus meeting on Thursday.

If Ryan can't sell his caucus on a compromise, centrist House Republicans are threatening to push forward with a discharge petition that would set up a series of immigration votes on the House floor.

If the House is able to pass legislation, it would kick the controversial issue back to the Senate months before a midterm election.

Senators rejected three separate immigration proposals earlier this year. The White House framework received the fewest number of votes, winning over only 39 senators.

"I went to immigration early this year. ... The Senate did not want to pass any particular version of it," McConnell added Wednesday night.

Trump sparked the months-long immigration debate last year when he decided to end the Obama-era Deferred Action for Childhood Arrivals program, which allows immigrants who came the country illegally as children to go to school and work.

Trump has demanded that any package combine the "Dreamer" protections with three other provisions: enhanced border security, including Trump’s U.S.–Mexico border wall; new limits on family migration; and the elimination of the diversity visa lottery.