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President Donald Trump has indicated that he's willing to back away from his demand that a government funding bill include money to build a wall on the Southern border, a move that could help clear the way for Congress to avoid a shutdown.

A senior administration official tells NBC News that the president is open to obtaining funding for the border wall in the regular appropriations process for 2018 later this year instead of insisting it be included as part of the large spending bill to keep the government's lights on past this week.

Such a development would be welcome news on Capitol Hill as congressional negotiators struggled to work past the administration's demands that few members wanted.

"It's good for the country that President Trump is taking the wall off the table in these negotiations," Senate Democratic Leader Chuck Schumer said in a statement Monday night after reports of the president's posture circulated. "Now the bipartisan and bicameral negotiators can continue working on the outstanding issues.”

If the funding is not to be a part of the current spending bill, however, Trump made clear Tuesday morning that he remains committed to building the wall.

Don't let the fake media tell you that I have changed my position on the WALL. It will get built and help stop drugs, human trafficking etc. — Donald J. Trump (@realDonaldTrump) April 25, 2017

The $1 billion request by the administration for a down-payment on the border wall, a project estimated to cost more than $20 billion, has been a major sticking point in negotiations to avoid a shutdown when the current funding runs out at midnight on Friday.

The president first expressed this new position during a private reception with conservative media Monday at the White House.

Sen. Thad Cochran, R-Miss., the top Republican on the Appropriations Committee, indicated Monday night, before Trump's stance was known, that talks had been progressing.

"There is some language in there [about a border wall] but it’s designed to be constructive in the process," he said. "I think we’ve made progress."

Trump's insistence on funding for a border wall in this bill was largely unpopular on Capitol Hill among both Democrats and Republicans.

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Democrats said that they would not support any bill that includes money for a border wall.

Republican Sen. Lindsey Graham, a member of the Appropriations Committee, had earlier cautioned the president against forcing Congress' hand on an issue so politically toxic at a time where Republicans are eager to show competency in running the government.

"If you can make this about better border security, the president’s in good shape," Graham said. "If he wants a 2,200 mile wall, I don’t think he’s going to get the votes to support that."

Democrats acknowledged that they'll support additional funds for border security, as long as it doesn't go specifically to building a wall.

Earlier in the day, the stand-off seemed as if it was becoming more entrenched as Trump, looking for a legislative victory before Trump's 100th day in office Saturday, took to Twitter to defend his position.

The Wall is a very important tool in stopping drugs from pouring into our country and poisoning our youth (and many others)! If — Donald J. Trump (@realDonaldTrump) April 24, 2017

Sean Spicer, White House press secretary, told reporters Monday that he “can’t guarantee” that there won’t be a government shutdown.

“I think that the work that [Office of Management and Budget] Director [Mike] Mulvaney and others have made in these negotiations has been very positive. They feel very confident that that won’t happen,” Spicer added.

Democrats feel that they have the upper hand, given that Republicans control the White House, the House, and the Senate, and would therefore own the political consequences.

"The president says he’s willing to shut down the government of the most powerful nation on earth if the U.S. taxpayers won't pay for a wall now that Mexico says they won’t," said Sen. Patrick Leahy, D-Vermont and top Democrat on the Senate Appropriations Committee, which is leading the negotiations. "I don’t think that’s a very smart thing to do."

Republicans insist that there won’t be a shutdown, and if they can’t reach agreement and pass a bill by Friday, they will pass a short-term spending bill for one or two weeks that will give negotiators more time to reach an agreement.

Health Care Compromises Continue to Evolve

While funding the government is the top priority for Congress this week, Republicans are making progress on an effort to revive their health care bill, the American Health Care Act.

Two House Republicans have floated a compromise that would enable states to waive requirements around pre-existing conditions, a component of the Affordable Care Act that Republicans promised would not be touched in any repeal of Obamacare.

Rep. Mark Meadows, R-N.C. and head of the conservative Freedom Caucus and Rep. Tom MacArthur, R-N.J. and co-chair of the centrist Tuesday Group, are working to bridge the gap between the conservative and moderate Republicans to help amass 216 Republican House votes in support of a compromise.

The latest iteration would allow states to ask the federal government for a waiver against providing coverage for pre-existing conditions if those states can show that they have alternate coverage options, such as a re-insurance program, a high-risk pool or federal-risk sharing program.

The new component is meant to appease the most conservative members of the House who say that mandates and regulations on how and who insurance companies can cover are driving up the cost of health coverage.

But many Republicans, as well as Trump, promised that any repeal of the Affordable Care Act would preserve coverage for pre-existing conditions.

Under the proposal from Meadows and MacArthur, people without existing insurance coverage could be charged more if they join the insurance market with health problems.

This proposal is building on an idea from last week that would allow states to apply for a waiver from providing essential health benefits in their insurance plans. Essential health benefits are services the federal government mandated that insurers must cover, like maternity care, hospitalization and emergency care.

It also would allow states to apply for a waiver on the community rating, a mandate that limits the amount health insurance companies can charge certain people. But increased charges can't be because of age, health and gender, essentially keeping intact the component known as the community health rating.