At the same time, Democratic leaders restated their openness Monday to providing some money for other types of border security improvements, suggesting a possible way out of the contentious standoff.

Facing a Friday deadline to keep the government open, congressional and administration negotiators are searching for ways to resolve their differences over what was a central campaign promise of Trump's. Notably, Republicans on the Hill and many top White House officials are not outright demanding that a down payment on the border wall -- which could cost tens of billions of dollars over time -- be made now.

Providing some money for border security -- personnel or equipment designed to crack down on illegal crossings -- but not for the wall itself, could provide a face-saving way for both sides to end for now their dispute on the issue and could clear the way for the massive government bill to pass both chambers ahead of Friday.

For instance, Treasury Secretary Steve Mnuchin speaking in the White House briefing room Monday declined to say if the President would insist on border wall funding in a final bill saying only that "the President is working hard to keep the government open and addressing various issues."

And when Press Secretary Sean Spicer was asked if Trump specifically expected there to be funding for the border wall in the funding bill, he didn't lay down the gauntlet and instead replied, "I don't want to get ahead of the negotiations they are ongoing. But the President's priorities have been very clear from the beginning."

Knowing they face unified opposition to the wall by Democrats, Republicans in the administration may now be getting the message that even Hill GOP members have been telegraphing throughout the negotiations -- it's not worth risking a shut down over the controversial issue.

"It is a divisive issue," Rep. Mike Coffman, a Republican from a swing district in Colorado, said in an interview on CNN. "I certainly support securing the border but I also support keeping the government open and I think this would cause the kind of showdown that would lead to a shutdown."

Despite these signals of a willingness to compromise by GOP negotiators, the President may be undermining their efforts -- or at least sending mixed messages -- by blasting out tweets, touting the wall.

"The Wall is a very important tool in stopping drugs from pouring into our country and poisoning our youth (and many others)! If the wall is not built, which it will be, the drug situation will NEVER be fixed the way it should be!" Trump wrote Monday on Twitter.

A senior Democratic aide familiar with the negotiations complained that the two sides on Capitol Hill continue to make progress, but Trump administration officials are the ones interjecting and holding things up, refusing to respond to an offer from Democrats on Capitol Hill to accept a package that includes more money for border security efforts, but does not include any resources to construct a wall.

"Congressional Republicans appear frustrated by the last-minute White House interventions, which have undermined their ability to achieve an agreement," the aide told CNN. "Speaker (Paul) Ryan and Leader McConnell will need to step up and get involved in the process directly in order to move the ball forward at this stage."

Sen. Chris Van Hollen, a Democratic member of the Senate budget committee, said in an interview on CNN's "Erin Burnett OutFront" that he was fine with including some money to support border security, but chastised Trump over failing to live up to his campaign promise to make Mexico pay for the wall.

"Border security is fine," Hollen said. "Wasting taxpayer dollars on a wall? No."

Van Hollen also stressed that the onus of any shutdown would be on the Republican Party, saying that Trump sounded like "an extortionist" to demand funding for his wall in the shadow of a government shutdown.

"Republicans have the White House," Hollen said. "They have both houses of Congress. I think it's going to be a big mistake for them to shut down the government because the President couldn't get Mexico to pay for the wall. ... He told the American people that we wouldn't have to waste our money on the wall."

In a conference call with reporters, House Minority Leader Nancy Pelosi, D-California, criticized Trump's late push for some funding for the wall now, which she said would be wrong if it was budgeted for at the expense of government programs like those that help young people, the elderly and the environment.

"He did not promise that he would take food out of the mouths of babies and seniors and education, clean air, clean water, scientific research off the table in a significant way in order for him to pay for his immoral, ineffective, unwise proposal of a wall," Pelosi said.

But she said she was open to some technology and other improvements at the border so long as they were not related in any way to the planning, prepping or building of the wall itself.

"So yes, if we have needs for the technology or the rest to help protect our border, let's see what that is," she said. "Our appropriators were well on a path to resolving their differences and finding their common ground, respecting each other's priorities until the White House intervened."

Democrats have publicly expressed support for more resources for border security as the two sides have worked on the must-pass funding measure. Since this package rolls together all the spending bills for various agencies they want to show that they back what many Americans views as a national security issue. But their earlier backing has been for the bipartisan process that appropriators have been working on -- not any talk about helping Trump pay for a wall that he argued Mexico would ultimately pay for during the 2016 campaign.

While the President may be working now to add something to show progress on the issue as he nears the 100-day mark of his tenure in office, Democrats on the Hill are making it clear it's a nonstarter.

Senate Minority Leader Chuck Schumer said Trump had thrown a "monkey wrench" into the sensitive budget talks when the White House demanded last week that border money be included in the government spending bill. Schumer said if Trump left congressional negotiators to cut a deal they could meet the Friday deadline.

"In my view if the President stepped out of it, we could get a budget done Friday," Schumer said.

Schumer urged Republicans to push the debate on the wall to a future bill even though he doesn't think it will pass then.

"We believe the Republican leaders should tell Donald Trump we can do this at a later time. I don't think it will pass," Schumer said "So instead of risking shutdown by shoving this wall down Congress's and the American people's throats, the President ought to let us come to an agreement and we're happy to debate this wall in regular order down the road once he has a plan. There is not a plan now."

Sen. John Cornyn of Texas, the second-ranking Senate Republican, opposes Trump's plan for a massive wall all the way across the border. But he does support building some physical barriers as called for by the Secure Fence Act, a 2006 law that was supported by many Democrats including Schumer.

"I think border security is important and certainly completing or at least making a down payment on something they've already voted for and supported seems to me to be kind of a no-brainer," Cornyn told reporters in the Capitol explaining that that there are still about 100 miles of the flexible fencing to be funded and built.

Cornyn was asked if that approach would save face for Democrats who could say they didn't fund the "wall" and save face for Republicans who can say they boosted border security.

"It sounds like everybody is looking to save face in one way or another. I don't really think that kind of posturing is necessary," he said. "I think they ought to just do our job, which is to fund the government through the end of the fiscal year and quit looking for reasons not to do so."

Senate Majority Leader Mitch McConnell, welcoming senators back from a two-week recess, said bipartisan talks were continuing but stopped short of predicting when a deal might be reached.

"Bipartisan talks continued through the state work period on the way forward on government funding legislation," the Kentucky Republican said. "Those discussions continue this week so we can complete our work on that issue very soon."

Negotiators are still working through issues on legislation that would wrap all the spending bills for the last five months on this fiscal year into one "omnibus" package. The fight over border wall money emerged as the most contentious issue, especially after Trump's budget director, Mick Mulvaney, floated an idea to link one dollar of Obamacare subsidy money to one dollar of border wall funding , a proposal flatly rejected by Democrats.

Aides from both parties appear confident that remaining policy issues can be resolved, but leaders from either side will need to brief rank-and-file members on any deal before moving ahead with votes before the deadline, and both agree they may need a stopgap bill to avoid any disruption of funding.

Pelosi and Schumer spoke on a conference call with Tom Perez, the Democratic National Committee chairman, that was designed to discuss Trump's first 100 days in office.