House Minority Leader Nancy Pelosi on Thursday flatly rejected the idea of approving funding for President Trump’s border wall in exchange for protections for illegal immigrant “Dreamers.”

“They’re two different subjects,” the California Democrat said.

Lawmakers on Capitol Hill are searching for a solution to a budget impasse, with Mr. Trump’s demand for $5 billion in border wall money the major hurdle right now.

The president has suggested he would force a partial government shutdown unless he gets the money he’s asking for. GOP leaders on Capitol Hill are interested in delivering, but Democrats, who maintain veto powers thanks to the Senate filibuster, say they can’t accept $5 billion.

Senate Minority Leader Charles E. Schumer has said his party would pass a Homeland Security spending bill that includes $1.6 billion — which was the administration’s original request back when it submitted its first budget. He also said another option would be to continue Homeland Security funding over from 2018, which included $1.6 billion for border security.

But he insisted that money would only go to fencing, and not to what Mr. Trump has envisioned as his wall.

Mrs. Pelosi said she’s pushing for that latter option of continuing the 2018 money into 2019.

“That’s pretty much where our position is now,” she said.

While there is no formal offer on the table, some analysts have speculated that Mr. Trump is desperate enough to get a win on border wall money that he would offer a path to citizenship to hundreds of thousands of illegal immigrants who are currently protected by the Obama-era DACA program.

That program is facing serious legal challenges, but Congress has stalemated on finding a more permanent policy to deal with DACA recipients, who were usually brought to the U.S. as children and are considered among the most sympathetic figures in the immigration debate.

One of the sticking points, though, is what to do about their parents — usually the ones who broke the law to bring them but who could stand to benefit if the children are granted full legal status.

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