President Trump and congressional Democrats remain sharply at odds over a spending package as Washington barrels toward a Friday at midnight deadline, leaving some on Capitol Hill increasingly worried that a Christmas government shutdown is in the making.

“I know of no plan,” Senate Majority Whip John Cornyn, R-Texas, said as he emerged from a leadership meeting late Monday, despite rumors and speculation of a possible way out of the legislative logjam.

The major sticking point continues to be Trump’s call for border wall funding. The president insists on $5 billion for a U.S.-Mexico wall, while Democrats don’t want to appropriate a dime more than $1.3 billion -- for fencing and other border security but not necessarily a wall.

But White House Press Secretary Sarah Sanders indicated Tuesday on Fox News that there’s room for compromise. She said on “America’s Newsroom” there are "other ways that we can get to that $5 billion," including a broader bill that would include $1.6 billion for a wall.

It's unclear whether that would sway Democrats.

Senate Democratic Leader Chuck Schumer thundered from the floor late Monday that with just days before the deadline, “President Trump still doesn’t have a plan to keep the government open.”

Schumer maintained that Trump does not have the votes for a wall, at least in the Senate.

“So everyone knows the situation: even with a Republican Congress, no threat or temper tantrum will get the president his wall,” he said.

But Trump suggested Monday that Democrats’ calls for border security ring hollow without support for the wall. “Anytime you hear a Democrat saying that you can have good Border Security without a Wall, write them off as just another politician following the party line. Time for us to save billions of dollars a year and have, at the same time, far greater safety and control!” he tweeted.

He followed up Tuesday morning: “Illegal immigration costs the United States more than 200 Billion Dollars a year. How was this allowed to happen?”

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It’s unclear where that cost estimate originates.

One possible escape hatch for Congress and the president would be to approve a short-term funding measure known as a “CR,” a time-tested tactic for delaying difficult funding fights without immediately resolving them.

One senior Senate Republican source said after Monday’s leadership meeting that a CR may be necessary, but noted that it appears Trump is running out the clock to build pressure.

“We are as unsettled as we have been for some time,” one GOP source said.

Fox News is told there are some efforts to try to convince Trump that a short-term spending bill is better. That would give Trump the opportunity to fight next year over the wall.

“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.

“There are not a lot of options and not a lot of certainty,” said one senior Republican source.

Several GOP sources suggest that the Trump administration has broad latitude to determine which workers are essential or not and may try to minimize the impact of a government shutdown. That would mean the shutdown could go for a while.

The ball seems to be in the president’s court: Lawmakers from both sides seem willing to punt into the New Year, and fight then.

Senate Democrats, meanwhile, continue to push the same plan offered during last week’s contentious Oval Office meeting with Trump. The proposal would wrap together six appropriations bills with a one-year spending measure for the Department of Homeland Security – including the $1.3 billion for border security. An alternative is a one-year funding package for all seven outstanding spending bills.

Fox News’ John Roberts and The Associated Press contributed to this report.