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The down-payment on construction of a border wall that President Donald Trump had sought has been dropped as part of the latest GOP proposal for a spending bill to prevent a government shutdown at the end of this week.

The latest offer by Republicans to Democrats in 11th-hour negotiations omits the $1 billion the White House had asked for to begin construction on a wall on the Southern border, three aides on Capitol Hill told NBC News. The request, a last minute demand, had threatened to blow up the negotiations as Democrats said that they would not pass a government funding bill with money for a wall included.

The proposal still includes $3 billion for border security — money for Immigration and Customs Enforcement and Customs and Border Patrol programs, including technology and road construction along the border.

Government funding for the current year is set to run out at midnight on Friday unless Congress can pass a bill to fund government programs for the next fiscal year.

“We're pleased he’s backing off,” Senate Democratic Leader Chuck Schumer told reporters Tuesday. “Now the bipartisan, bicameral negotiations to reach an agreement that both parties can be proud of can move forward.”

Trump told a group of conservative media Monday night that he wouldn’t push for funding for the border wall in this short term bill but would wait until the fall when negotiations take place for spending in 2018.

If the pending spending bill does not include the down-payment to begin construction of the wall, White House Press Secretary Sean Spicer said Tuesday that president's "priorities have not changed. There will be a wall built."

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"The wall gets built, 100 percent," Trump said in brief remarks Tuesday afternoon.

Related: Trump Signals Willingness to Drop Border Wall From Budget Standoff

Sen. Lindsey Graham, R-S.C., was at the White House Monday night and said that Trump seemed to understand that $1 billion for a $20-plus billion project isn’t worth a government shutdown at this point.

“I got the sense that he’s not going to take this fight too far,” Graham said. “That he understand border security’s important and the wall’s important but he’s not going to overplay his hand.”

A senior Republican aide said that since Trump took the wall off the table, it’s up to Democrats as to whether they are willing to cooperate.

“Here’s the challenge to the Democrats ... are you going to overplay your hand?” Graham asked rhetorically. “I don’t know what Schumer wants. If he wants a government shutdown, be careful what you wish for.”

The next big item for negotiators is funding for a subsidy in the Affordable Care Act that helps low-income people afford health care. The Trump administration has indicated they want to withhold funding — a move that would further destabilize the insurance market, which Trump says would help speed the collapse of Obamacare.

“It’s still part of the discussion,” said Sen. John Barrasso, R-Wyoming of that provision. “It’s an ongoing discussion.”

Other sticking issues include money for coal miners’ health care and pensions, programs set to expire if they aren’t extended.

Senate Majority Leader Mitch McConnell told reporters that he’s supportive of extending the health care program for miners but didn’t answer a question on if he supports the pension extension in this particular funding bill.

Another issue being debated is the Trump administration's request for an additional $30 billion in defense spending.

Time is running out. Any bill must pass both chambers of Congress before Friday at midnight. If negotiators don’t reach a deal or complete the logistics of passing a major bill, Congress could pass a short-term extension that allows for more time.

We’re at “the point you need to decide if you have the time to get all the paperwork together. I would think we’ve had plenty of time to work on this and a short term extension to have more time to negotiate would not be something that I recommend, but a short term extension to put everything together — this is probably the last day you could decide that,” said Sen. Roy Blunt, R-Missouri, and member of leadership.

But Sen. Patrick Leahy, D-Vermont, who is the top Democrat on the Appropriations Committee, which is leading the negotiations, said he is getting frustrated.

“We had this stuff all wrapped up in November. My God, how long does it take to get to yes?” Leahy said.