Democratic leaders in Congress say they have no interest in making a deal with President Trump to end the government shutdown if it includes new money for his border wall.

But cracks within the Trump resistance are starting to show, with Democratic lawmakers and influential liberal opinion makers imploring House Speaker Nancy Pelosi and Senate Democratic Leader Chuck Schumer to at least meet Trump at the negotiating table. Some are even arguing they should agree to border wall funds.

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“Give Trump the money,” Minnesota Democratic Rep. Collin Peterson said on local radio Tuesday. “I’d give him the whole thing…and put strings on it so you make sure he puts the wall where it needs to be. Why are we fighting over this? We’re going to build that wall anyway, at some time.”

Michigan Democratic Rep. Elissa Slotkin told a local news outlet that Democratic leaders need to “get in the damn room” because the issue will not resolve itself. Slotkin said she’s “absolutely willing” to work on negotiating a deal involving border security.

Still, Fox News has learned that newly elected New York Rep. Alexandria Ocasio-Cortez, an influential voice among the progressive left, spoke to the House Democratic Caucus on Wednesday morning and encouraged Democrats to continue to apply pressure on Senate Majority Leader Mitch McConnell to end the government shutdown without new wall funding.

The government partially shut down in December after Congress failed to pass a spending package. Trump is demanding $5.7 billion for a barrier on the southern border with Mexico, something Democratic leaders are rejecting.

Over the weekend, the president offered a compromise deal to Democrats to re-open shuttered government agencies, saying he is prepared to back a three-year extension of protections young people brought into the country illegally as children, and extend protections for 300,000 recipients of the Temporary Protected Status (TPS) program in return for the border money.

Though some Democrats once pushed for those same protections for immigrants, Pelosi and Schumer have indicated they aren’t willing to budge on border wall funding.

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But the pressure is growing for the Democrats to negotiate.

Some centrist Democrats led by Rep. Elaine Luria of Virginia are encouraging Pelosi to respond to Trump’s offer with a counter-proposal.

“We promised our constituents that we would seek bipartisan solutions, and we feel that this proposal would gain bipartisan support and allow a transparent process to evaluate the true needs of border security and provide much-needed reform to our immigration system,” the draft letter, posted online by Luria, states.

The group suggests lawmakers immediately reopen the government without border wall funding, but with the pledge that House committees will start debating border security. It's unclear whether Trump would entertain the idea -- the president has said he will only support a spending package that includes wall funding.

Other influential liberal voices, who often oppose the president, are calling on Democrats to work with Trump on his latest offer.

The editorial board of the Washington Post over the weekend called on Democrats to come back to the table. In an editorial titled “Make a deal. Save the dreamers,” the paper argued Trump “should not be rewarded for having taken the government hostage” but said Trump’s offer to compromise “should be welcomed.”

Walter Isaacson, the author and former CEO of the Aspen Institute, tweeted that Democrats “should take the deal.”

“DACA (the most impt moral issue) will inevitably stay in place,” Isaacson tweeted. “His base will rebel against him. The border funding will never lead to a real wall. Steel fences in a few more locations not that bad a thing for US — or for Dems.”

The pressure comes as two different votes are set for Thursday in the Republican-controlled Senate with the aim to end the partial government shutdown. One vote will be on a bill reflecting Trump's demand for border wall funding in exchange for temporary protections for some immigrants.

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A second vote is set for a measure already passed by the Democrat-controlled House to reopen the government through Feb. 8. It doesn't allow money for a border wall but gives bargainers more time to talk.

Neither bill is expected to advance under Senate rules requiring at least 60 votes.

Meanwhile, House Democrats are considering drafting a new proposal to provide Trump with options for securing the border that don't involve a wall between the U.S. and Mexico. Democratic Rep. Hakeem Jeffries of New York said Wednesday that personnel, technology and other options "are the things that would actually improve our border security." The proposals are likely to be drafted into a sweeping Homeland Security bill.

Fox News’ Chad Pergram, R.N. White and The Associated Press contributed to this report.