Some expressed befuddlement at Trump’s strategy, while others sidestepped his comments, marking a new rift between the president and his party on Capitol Hill with just weeks left at the helm of both chambers of Congress.

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“I don’t understand the ­strategy, but maybe he’s figured it out and he’ll tell us in due course,” said John Cornyn (Tex.), the No. 2 Senate Republican. “But I don’t understand it.”

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The disconnect reflects the divergent priorities of Trump and Republicans in Congress during the twilight of their two-year grip on the federal government. While Trump made the wall a signature issue in his 2016 campaign, congressional GOP leaders have displayed less enthusiasm for it.

The divide comes weeks after a difficult midterm election for the GOP, in which Democrats won control of the House. The outcome presented Trump with even longer odds of securing wall funding in the new year.

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Still, John Thune (S.D.), the third-ranking GOP senator, said there was no scenario under which he would be proud to shut down the government.

“It would not be good,” Thune said.

Pressed on whether Trump’s comments were helpful to the negotiations, Thune answered obliquely.

“The president has his own style and way of negotiating,” he said. “The only thing I would say is, it’s just simple math — that you’ve to got to get 60 votes in the Senate, and that’s going to require Democrats.”

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In the wake of Trump’s contentious Oval Office meeting Tuesday with House Minority Leader Nancy Pelosi (D-Calif.) and Senate Minority Leader Charles E. Schumer (D-N.Y.), Republicans found themselves no closer to bridging the gap between Trump’s demand for $5 billion for his border wall in 2019 and the $1.3 billion Democrats are willing to spend on border fencing.

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Instead, Republicans confronted a dilemma of Trump’s own making after he flipped the script by telling Pelosi and Schumer he’d be “proud to shut down the government for border security.”

The president’s off-the-cuff declaration in the televised Oval Office confab left talks at a virtual standstill and deprived Republicans of their ability to blame Democrats for a partial shutdown that could come at midnight Dec. 21, just before Christmas.

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Republican lawmakers and members of Trump’s own administration have been talking for weeks about a “Schumer Shutdown” as they maneuvered to pin the blame on Democrats if a partial shutdown occurs. Democrats were delighted that Trump had taken ownership of a shutdown, and Republicans were forced to acknowledge that the president’s comments undermined their own efforts.

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“I’m on the record saying numerous times I think a shutdown is a fool’s errand. Every shutdown we’ve been in, nobody wins. So I’m very discouraged by that,” said Sen. Shelley Moore Capito (R-W.Va.).

“I think he wants to reach an agreement, and I think he’ll realize — as he thinks about it — that a shutdown is really not going to gain anything for his position and, in a lot of ways, is more damaging to the American people,” Capito added.

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Pelosi and Schumer urged the president in Tuesday’s meeting not to pursue a shutdown and instead take a deal that would provide $1.3 billion for border fencing by extending current levels of funding. Trump long has promised that Mexico would pay for the wall, a claim he repeated privately to Pelosi on Tuesday, saying the money could come from the newly renegotiated North American trade agreement. Pelosi dismissed that idea.

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In the aftermath of the Oval Office meeting, House Republicans were struggling with whether to hold a vote on a spending bill containing $5 billion for the wall. It’s a priority for many conservatives in their final days in the majority, and it took on added urgency after Pelosi and Trump argued publicly Tuesday about whether it could pass the House, with Pelosi claiming it couldn’t and Trump insisting it could.

House GOP leaders claimed Wednesday to have the votes, but some questioned the wisdom of holding a vote that would face certain rejection in the Senate. And the risky proposition would come in the waning days of a lame-duck session, when it could be difficult to corral scores of defeated and retiring House Republicans who have been showing up only intermittently to vote.

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“Do we have the votes for a measure that includes $5 billion for the wall? Yes,” said Rep. Patrick T. McHenry (N.C.), a member of the House GOP leadership. “The question of whether to do it is a question of wisdom and strategy and tactics, and it’s highly debatable about whether that’s the right move.”

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That view was disputed by some House conservatives who campaigned along with Trump on delivering the wall and feel they must do it now before they fade into the minority. A few hard-liners said they were willing to back Trump even if his demands push the government into a partial shutdown.

“The president’s challenge is, and I’m with him on this, is that he needs to have $5 billion locked in and assured before the gavel falls on the 115th Congress,” said Rep. Steve King (R-Iowa).

“He said he would be proud to own it; that might have been a little hyperbolic,” King added. “But this is a line he’s drawn, and I’m going to defend it.”

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The impact of any shutdown would be limited because about 75 percent of the federal government’s discretionary budget has been funded through next September. That includes major agencies like the Pentagon and the Health and Human Services Department.

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And there would be no impact on the payment of Social Security, Medicaid or Medicare benefits because those programs fall under “mandatory” spending that is paid out without annual congressional approval. Mandatory spending makes up about 70 percent of federal spending.

In light of those facts, several Republicans downplayed the potential impact of a partial shutdown, suggesting that even if it did happen it wouldn’t be such a big deal.

“The fact is, the vast majority of the government is not going to be shut down under any scenario,” said Sen. Patrick J. Toomey (R-Pa.). “So there’s this little tiny sliver, and within that universe, anybody that is an essential employee still works. So I think this has all gotten a lot overblown.”

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Still, the agencies that remain to be funded could be hit hard.

The Interior, Agriculture, Justice, Commerce, Transportation and State departments and NASA could be forced to send thousands of workers home without pay until an agreement is reached. This could lead to major disruptions and delays in services, although the precise implications will not be clear until each agency determines how it will operate after funding lapses.

Within Homeland Security, most employees are exempt from a shutdown and would report to their jobs regardless, including workers at the Federal Emergency Management Agency, Border Patrol, Coast Guard, Transportation Security Administration, and U.S. Immigration and Customs Enforcement agency. These workers could go unpaid if the shutdown dragged on, but they would eventually get back pay once it was over.

“We’re at an impasse at the moment,” said Senate Appropriations Chairman Richard C. Shelby (R-Ala.). Shelby said a shutdown is “probably more than possible right now, probably getting toward probable — unless something happens.”