During a brief period of questions, an unidentified reporter asked Trump whether he would be willing to sign a budget deal without funding for a border wall.
The move from GOP leaders comes as Capitol Hill scrambles to pass a government funding measure by midnight Friday to avert a shutdown on President Donald Trump's 100th day in office.
Though a White House official told a CNN reporter that the money for the wall would indeed be included in the spending bill, there is doubt since Congress clearly can not agree and a government shutdown would be a massive political problem for Republicans.
"But it looks like, from here, right here, right now, it looks like President Trump is caving on his demand for a measly $1 billion in the budget for his wall".
A partial shutdown would start on Saturday, Trump's 100th day in office.
Mr Trump campaigned throughout the country a year ago promising a wall across the entire 2,200-mile southern border, promising that Mexico would pay for it.
Senate Democratic leader Chuck Schumer said in a statement on Monday night that it is a good thing for the country that Trump is taking the wall budget off the table in these negotiations.
He continued: "Trump, I'm sure, does not ever think he caves on anything".
"We're moving forward on reaching an agreement on a bipartisan basis", Senate Majority Leader Mitch McConnell, R-Ky., told reporters, adding that he hoped that an agreement to fund the government through September can be reached in the next few days. The president did not address whether he would still demand Congress fund the wall in this week's spending bill.
The White House had offered to include $7 billion in Obamacare subsidies that allow low-income people to pay for healthcare insurance in exchange for Democratic backing of $1.5 billion in funding to begin construction of a barrier on the U.S. -Mexico border.
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The court quickly reversed course, but its widely condemned move still galvanised the opposition. "I'm staying here until 6 p.m". The opposition blames Maduro's regime for the deaths, whereas Maduro blames the opposition.
"The wall's going to get built, folks".
Congressional leaders in both parties expressed optimism that they'll be able to avoid a costly and damaging government shutdown, either by striking a deal by the Friday deadline or passing a short-term funding extension to finish the deal next week.
Luis Videgaray, Mexico's foreign relations secretary, joined the chorus of wall detractors, calling the president's plan an "unfriendly, hostile" act that undermines the good relationship enjoyed by the USA and Mexico.
A Republican effort to repeal and replace Obamacare imploded in Congress last month and the White House said on Monday that another vote could not come for weeks.
"I will say Secretary Kelly, formerly General Kelly, is doing an incredible job".
Democrats have said they would be comfortable with some additional funding for border security and surveillance. But the White House leader often said that Mexico would pay for the wall, while the Mexican president has said his country will not do that.
Even though the wall may be indefinitely delayed, it seems that the issue will remain at the forefront of policy, especially if Trump's pals in the Senate introduce go-nowhere bills that will keep the wall in the news cycle.
Lawmakers have warned that a stopgap measure, known as a continuing resolution, may be needed to give Congress breathing room to finalise the spending details.
He accused the Democrats of being opposed to the wall, and ignoring the fact that it will stop drugs and "very bad MS 13 gang members". "If he didn't, I'm glad it worked out", Schumer said.
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