Senate Majority Leader Mitch McConnell announced on Wednesday that a continuing resolution to fund the government through Feb. 8 will be introduced later this morning.

"Later this morning, we’ll introduce a continuing resolution that will ensure continuous funding for the federal government. The measure will provide the resources necessary to continue normal operations through February 8," McConnell said in remarks on the Senate floor.

That resolution will not include $5 billion in funding for the border wall that President Donald Trump said was a must in order to have his approval in order to fund key parts of the federal government before they run out of operating authority on Friday.

Both House and Senate Democrats have indicated they will not oppose a stopgap funding measure through early February, two Democratic sources told NBC News Tuesday night.

The White House in recent days has softened its stance and signaled that Trump will not shut down the government over border wall funding, but that doesn't mean he's backing down, both he and officials said.

"We have other ways that we can get to that $5 billion," White House press secretary Sarah Sanders told Fox News on Tuesday. "We don't want to shut down the government, we want to shut down the border from illegal immigration."

White House counselor Kellyanne Conway told Fox News on Wednesday that should Trump approve a short-term government funding package, it "doesn't mean the president is backing down from an essential promise."

And on Twitter Wednesday morning, Trump tweeted: "One way or the other, we will win on the Wall!"

Trump was the only major player in the government funding debate who seemed willing to shut down the government over $5 billion in funding for his long-promised wall along the U.S. southern border. While he originally insisted that Mexico would pay for the wall, he now claims Mexico will pay for it through his revamped trade agreement with the nation. The White House has struggled to explain how exactly that would happen.

Meanwhile, lawmakers have now signaled that they think chances of a shutdown are very low.

"I don't know yet from the White House what their plan is on a continuing resolution," Republican Sen. James Lankford of Oklahoma told MSNBC Wednesday morning. "Any shutdown that occurs obviously would be very much smaller than what has been done in the past."

He added that having to "punt" on a larger funding bill until early next year is "exceptionally frustrating."

White House officials told NBC News that Congress needs to pass something to show the administration before they indicate whether the president will support it. Trump will make a decision after seeing the plan, White House deputy press secretary Hogan Gidley said.

It's a strikingly different tone than the one Trump struck during a televised negotiation with House Democratic leader Nancy Pelosi, D-Calif., and Senate Minority Leader Chuck Schumer, D-N.Y., last week. Trump said then that he would be "proud to shut down the government" if he did not receive the wall funding he wanted.