Congressional leaders resumed negotiations Tuesday to avert a partial government shutdown at the end of the week, as the White House indicated it was looking for alternative ways to fund President Trump’s signature campaign promise of a border wall without a government funding lapse.

Trump had demanded $5 billion in funding for the wall, estimated to cost between $20 billion and $25 billion; Democrats countered with $1.3 billion -- on the condition it was for fencing and not a wall.

A workable compromise has not yet emerged, but options are floating around Capitol Hill. As Washington barreled toward a Friday shutdown deadline, a Senate Democratic aide told Fox News that Senate Majority Mitch McConnell, R-Ky., proposed $1.6 billion for border security (which would include fencing, not a concrete wall as Trump promised his supporters) and a $1 billion “slush fund” for Trump to use for his immigration agenda.

McConnell later said that offer was rejected by Democrats, but told reporters he was confident there would not be a Christmas shutdown.

TRUMP, DEMS DIG IN AS GOVERNMENT SHUTDOWN LOOMS: 'I KNOW OF NO PLAN'

Senate Minority Leader Chuck Schumer, D-N.Y., told reporters that he didn’t believe McConnell’s offer would have passed either chamber. He also said that any “reprogramming” of money from other agencies would require Congressional approval.

“They’re not getting it,” he said.

At the White House, there were signs that the administration was backing down on its previous tough demands for the $5 billion funding. White House Press Secretary Sarah Sanders told reporters they were “disappointed” that the Senate hadn’t voted on anything, and said the White House was looking at “every avenue” to find additional funding -- including having funds redirected or "reprogrammed" from other departments.

“President Trump has asked every one of his cabinet secretaries to look for funding that can be used to protect our borders and give the president the ability to fulfill his constitutional obligations to protect the American people by having a secure border,” she said.

Sanders did not specify where they were looking for funding, and also didn’t say whether Trump would accept a lower figure if the White House could find other money from other agencies. Earlier, on Fox News' “America’s Newsroom,” she said there was room for compromise and there are "other ways that we can get to that $5 billion."

"At the end of the day, we don't want to shut down the government," Sanders said. "We want to shut down the border from illegal immigration."

The rhetoric was toned down significantly from last week, when Trump had scrapped with Schumer in front of the cameras in the Oval Office -- where Trump said he had no problem shutting down the government.

"If we don't have border security, we'll shut down the government," he said.

Anything significantly below $5 billion, particularly if it explicitly ruled out a concrete wall, would likely be seen by immigration hardliners in Trump’s base as a failure by Trump and Republican leaders. Even if the wall was included in the funding (under McConnell’s proposal it would not), then it would mean the wall had been funded by only a tenth -- halfway through Trump’s first term.

Democrats, meanwhile, welcomed the White House’s apparent wobble on the shutdown, with House Minority Leader Nancy Pelosi calling it a “good sign” that the White House was backing off.

Fox News is told there are some efforts to try to convince Trump to consider a short-term spending bill. That would give Trump the opportunity to fight next year over the wall, though Democrats take control of the House next month.

“I’m not sure that will sell,” one source cautioned. Some in the White House’s legislative affairs shop are coming to Capitol Hill to discuss options, though multiple Republican sources on Capitol Hill say they are running out of time.

Schumer told reporters that if McConnell put a short-term bill on the Senate floor, “we would have a serious discussion about it.”

Washington has a deadline of Friday night to avoid a shutdown. Without a resolution, more than 800,000 government workers could be furloughed or sent to work without pay, disrupting government operations.

Fox News' Chad Pergram and Judson Berger and The Associated Press contributed to this report.