In this Saturday, April 2, 2016 file photo, supporters of Republican presidential candidate Donald Trump chant, "Build that wall," before a town hall meeting in Rothschild, Wis. Associated Press/Charles Rex Arbogast Whether the federal government shuts down on Friday could hinge on whether Congress includes funding for President Donald Trump's proposed border wall in legislation to keep the government funded.

Trump and administration officials have in recent days talked up the possibility of including funding for a wall along the US-Mexico border. That could set up a showdown with Democrats and even members of his party as the clock ticks toward a shutdown.

Asked by The Associated Press on Friday whether he would sign a bill that did not include funding for the wall, Trump was noncommittal.

"I don't know yet," Trump said. "People want the border wall. My base definitely wants the border wall. My base really wants it — you've been to many of the rallies. OK, the thing they want more than anything is the wall."

The president also used Twitter over the weekend and on Monday to lay the groundwork for a push to fund the wall.

"The Democrats don't want money from budget going to border wall despite the fact that it will stop drugs and very bad MS 13 gang members," Trump tweeted on Sunday. He followed that up with a tweetstorm on Monday about the importance of the wall.

Trump also mentioned his campaign promise to require Mexico to pay for the wall, a proposition Mexican officials have flatly refused.

"Eventually, but at a later date so we can get started early, Mexico will be paying, in some form, for the badly needed border wall," Trump tweeted.

Administration officials who made the rounds on the Sunday political talk shows sounded more cautious about including border-wall funding in the spending bill.

Chief of Staff Reince Priebus told NBC's "Meet the Press" that if there were "enough as far as flexibility for the border wall and border security" in the spending bill, the administration would "be OK with that."

On the other hand, Homeland Security Secretary John Kelly told CNN's "State of the Union" that Trump had been "pretty straightforward about his desire and the need for a border wall" and that funding for it was a vital element of the president's negotiations on the shutdown.

"So I would suspect he'll do the right thing for sure, but I would suspect he will be insistent on the funding," Kelly said.

Mick Mulvaney, the director of the Office of Management and Budget, has proposed a deal — the Trump administration would include in the bill $1 in funding for Obamacare's cost-sharing reduction payments, which help mitigate losses for insurers, for every $1 in funding for the wall.

"Right now, that's the offer that we've given to our Democratic colleagues," Mulvaney said.

Trump also seemed to hint at this idea in a tweet on Sunday.

"Obamacare is in serious trouble," Trump said. "The Dems need big money to keep it going - otherwise it dies far sooner than anyone would have thought."

Democrats, however, blasted the idea. Senate Minority Leader Chuck Schumer's office said the White House's suggestion was a "gambit to hold hostage healthcare for millions of Americans."

"The US government is supposed to take care of its citizens, and, according to the president, Mexico is supposed to pay for the wall," a representative for Schumer said. "If the administration would drop their eleventh-hour demand for a wall that Democrats, and a good number of Republicans, oppose, congressional leaders could quickly reach a deal."

While Schumer and Democrats alone cannot block a funding bill, budget hawks in Congress' conservative factions, like the House Freedom Caucus, could balk at increasing the deficit to fund the wall.

Given the GOP's inability to pass its bill to overhaul Obamacare because of intraparty disagreements, the passage of the spending bill is questionable. Thomas Block, a Washington policy analyst at Fundstrat, described the problem in a note to clients on Monday:

"In the House, there is a group consisting of Tea Party and Freedom Caucus Republicans who believe that almost any spending bill is too large for them to support. Therefore, Speaker Ryan is likely going to need some Democratic support to get a bill passed. The problem is that no Democrats will support a bill that contains the president's stated priorities.

"Furthermore, many Republicans want to use the spending bill to stop all funding for Planned Parenthood, a clear poison pill as far as most Democrats are concerned."