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 Renard FoxxTo address America's crumbling infrastructure, follow Britain's lead Report: Chao has used government planes seven times this year Week ahead in tech: Lawmakers turn focus to 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 Antonio RubioRyan pledges 'entitlement reform' in 2018 Richard Gere welcomes lawmakers' words of support for Tibet Dem lawmaker gives McConnell's tax reform op-ed a failing grade 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 Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery 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 Andrew BoehnerJohn Feehery: A political forest fire Trump's pick for Federal Reserve chief is right choice at right time The two-party system is dying — let’s put it out of its misery 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.”