President Obama’s outgoing Transportation Secretary Ray LaHood, a former GOP House member, says Republicans won’t win another White House race without a deal on major immigration legislation.

LaHood spoke to The Washington Post as he prepares to hand over the Cabinet job to Anthony FoxxAnthony FoxxDC mayor touts progress in reducing traffic deaths Toll roads poised to boom under Trump plan Transportation chief urges Trump to press forward on self-driving cars MORE, the Charlotte, N.C. mayor that the Senate last week confirmed to replace him.

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“We will not win another presidential election as Republicans,” LaHood told the Post, “unless we do something to fix the broken immigration system.”

LaHood urged the House GOP to take a page from the book of Sen. Marco RubioMarco RubioOvernight Defense: Commander calls North Korea crisis 'worst' he's seen | Trump signs VA order | Dems push Trump to fill national security posts What’s with Trump’s spelling mistakes? Boeing must be stopped from doing business with Iran MORE (R-Fla.), who helped craft the bipartisan plan the Senate approved last Thursday. If they don’t, LaHood warned, “this is going to be the death knell for Republicans winning national elections for decades.”

Some analysts see an immigration deal as crucial for Republicans’ national political viability going forward. Hispanic voters overwhelmingly favored President Obama in his race against GOP White House hopeful Mitt Romney last year.

Speaker John BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE (R-Ohio) has said he will not shepherd an immigration bill through the House that does not have a majority of the chamber’s Republicans behind it, a threshold that complicates prospects for a House-Senate deal.

LaHood suggested that BoehnerJohn BoehnerLobbyists bounce back under Trump Business groups silent on Trump's Ex-Im nominee Chaffetz won't run for reelection MORE may need to buck his conference for the good of the party nationally.

“Look, this takes real courage,” he told the Post. “This takes the possibility of falling on [Boehner’s] sword for a greater good — for a greater good for the party, not for himself.”