In the wake of the unexpected, dramatic on-camera dust-up between President Trump and Democratic leaders Chuck Schumer and Nancy Pelosi in the Oval Office on Tuesday, top Republicans are rallying behind the president's calls for funding a southern border wall -- even if it could mean closing the government just days before Christmas.

"If we don't have border security, we'll shut down the government," Trump told Schumer and Pelosi, as the White House photo op quickly went off the rails and Vice President Mike Pence looked on sternly and silently. Afterwards, Pelosi reportedly mocked the president in a private meeting on Capitol Hill with fellow Democrats, saying "it's a manhood thing for him -- as if manhood could ever be associated with him."

Fox News has confirmed that, in a deliberate show of support for Trump following the nationally televised showdown, House Republican leaders are considering sending a bill that would provide $5 billion in funding for the wall to the floor for a vote.

Rep. Patrick McHenry, R-N.C., told Fox News Tuesday afternoon that "we can pass it," although he clarified that GOP leaders have not yet whipped the votes.

A senior House GOP aide separately told Fox News that Republicans are confident the measure would pass, which would force Schumer and Senate Democrats to either approve the funding or risk being blamed for any ensuing government shutdown.

"If I were the president, I would dig in and not give in," South Carolina Republican Sen. Lindsey Graham, a Trump ally who has sparred with the administration recently over Saudi Arabia policy, told Fox News on Tuesday.

Graham said he had spoken to Trump on the phone and that "he seems pretty dug in" on his position. The president vowed during the campaign that Mexico would pay for the wall, but has since claimed the country will reimburse the U.S. for some of the cost.

In January, Schumer was slammed as a "coward" by fellow progressives after he forced a government shutdown by insisting that any temporary spending bill to keep the government fully operational include permanent protections for the so-called DREAMers -- immigrants brought illegally to the United States as children. Schumer backed off just days later in exchange for Republican promises to consider the matter in the future.

Trump told reporters in a pool spray at the White House later Tuesday that "Chuck's problem is that when we last closed down, that was his idea, and honestly he got killed, and so he doesnt want to own it. And I said, rather than us debating who's owning it, I'll take it. If we close down the country, I will take it. Because we're closing it down for border security, and I think I win that every time."

The president called the White House meeting a "friendly" encounter" on issues that included his bipartisan criminal justice reform progress. And Trump emphasized his belief that illegal immigrants pose a "tremendous medical problem" by bringing "communicable disease, tremendous probems that "people don't want to talk about."

He asserted that the public is willing to tolerate a shutdown for border security.

"If we have to close down the country over border security, I actually like that in terms of an issue, but I dont want it to be an issue. It's not really an issue, it's something the country needs, it's common sense. We need security from drugs that are pouring into our country."

The president was not alone in that assessment. Responding to critics who predicted Republicans would be blamed for the standoff -- Pelosi referred to the possible closure of government as a "Trump shutdown" in the Oval Office -- Graham also appeared undeterred.

“I’m fine with being the party that's going to secure our border now," Graham said. "We’re not going to wait any longer. We’re not going to keep kicking the can down the road.”

In a statement Monday evening, the conservative House Freedom Caucus officially called for that immediate funding and said it was Republicans' "last chance" to secure the border before Democrats retake the House in January.

Graham, as well as GOP Senate Majority Leader Mitch McConnell, noted that Schumer and other Democrats have supported similar border bills in the past, including a 2006 law that authorized hundreds of miles of fencing along the southern border.

"I will tell you I think it is a reasonable request to ask for more money than the Congress has appropriated in light of the fact that every member of Congress on the Democratic side has voted in the past for a lot more money for border security," Graham said. "You shouldn't be denied the money because you won the election and they don't like it. This arrogance toward Trump has to stop."

"If I were the president, I would dig in and not give in." — Sen. Lindsey Graham, R-S.C.

McConnell, R-Ky., told reporters that "we dont know how long discussion over government funding is going to go on" and that lawmakers were "sort of hoping for Christmas miracle."

He noted that representatives and senators are generally more conciliatory over the holidays, as they seek to head home rather than stay in Washington debating and passing bills. A farm bill that mostly avoids partisan areas of contention like food stamps is set for passage Tuesday afternoon in the House, separate from the government spending bill.

CLASH FOR THE CAMERAS: TRUMP OVAL OFFICE MEETING WITH SCHUMER, PELOSI BOILS OVER

"I hope that’s not where we end up," McConnell told Fox News, referring to a government shutdown. "I know it was a spirited discussion [in the Oval Office.] I would still like to see a smooth ending."

He added: "In the meantime, we're going to start processing these various items that are listed, beginning with the farm bill later today. And so if that occurs, there won't be any need to put any of those items into a government funding bill, so I can't predict when an agreement will be reached on the government funding bill, so we're just going to keep processing these issues as rapidly as they can as we can.

"And as I said, I'm sort of hoping for a Christmas miracle here, that we'll have a level of cooperation that we don't normally have in getting bills across the Senate floor."

Up against a Dec. 21 deadline to fund the government, Pelosi and Schumer have urged Trump to support a measure that includes a half-dozen government funding bills largely agreed upon by lawmakers, along with a separate measure that funds the Department of Homeland Security at current levels through Sept. 30.

The homeland bill includes about $1.3 billion for fencing and other security measures at the border.

If Trump rejects that, Democrats are urging a continuing resolution that would fund all the remaining appropriations bills at current levels through Sept. 30.

“We gave the president two options that would keep the government open,” Pelosi and Schumer said in a statement after the meeting. “It’s his choice to accept one of those options or shut the government down.”

Pelosi, who is seeking to become House speaker when the new Congress convenes in January, said she and many other Democrats consider the wall “immoral, ineffective and expensive."

The sit-down between Trump, Schumer, and Pelosi quickly escalated, in public, as Trump allowed the press to attend the start of it. Trump began by repeatedly telling Pelosi, the House Democratic leader, his party is limited in what it can do because it will take Democratic support to pass anything through the Senate.

Schumer then raised his voice as he claimed the Senate could pass measures to keep the government running regardless.

"If it's not good [on] border security, I won't take it," Trump shot back.

Pelosi and Schumer repeatedly urged the president to take the meeting private, but not before he declared he's "proud to shut down the government for border security" and will "take the mantle."

WILL MILITARY BUILD BORDER WALL IF DEMS REFUSE TO PASS FUNDING BILL?

Pelosi noted, "this has spiraled downwards."

The meeting broke up roughly a half-hour after the cameras stopped rolling. The very-public discord leaves unclear whether the two sides can come to an agreement to keep the government running before a looming Dec. 21 deadline.

Pelosi, speaking to reporters afterwards, claimed they left things “in a pretty good place.” But the White House put out a statement after the meeting saying “major disagreement remains on the issue of border security and transparency,” despite their "constructive dialogue."

Hours before the meeting, Trump threatened to have the military “build the remaining sections” of the U.S.-Mexico border wall, appearing to revive a call to use Pentagon money to finish the project.

"To date, there is no plan to build sections of the wall," a Defense Department spokesperson told Fox News Tuesday afternoon. "However, Congress has provided options under Title 10 U.S. Code that could permit the Department of Defense to fund border barrier projects, such as in support of counter drug operations or national emergencies."

Fox News' Chad Pergram, Alex Pappas, Mike Emanuel, Jason Donner, Judson Berger, and The Associated Press contributed to this report.