Graham: Trump giving up on border wall fight would be the 'end of his presidency'

Sen. Lindsey GrahamLindsey Olin GrahamSenate Democrats pump brakes on new stimulus checks Comey, Rice, Clapper among GOP senator's targets for subpoenas amid Obama-era probe Schumer: GOP should 'stop sitting on their hands' on coronavirus bill MORE (R-S.C.) on Wednesday cautioned President TrumpDonald John TrumpMinneapolis erupts for third night, as protests spread, Trump vows retaliation Stocks open mixed ahead of Trump briefing on China The island that can save America MORE against giving in on his demand for funding for his proposed U.S.-Mexico border wall, claiming that doing so would likely be "the end of his presidency."

“He’s not going to sign a bill that doesn’t have money for the wall. I can tell you exactly how this is going to end. The president is going to challenge Democrats to compromise and if they continue to say no, they’re going to pay the price with the American people," Graham said during an appearance on Fox News's "Hannity."

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“If he gives in now, that’s the end of 2019 in terms of him being an effective president," he continued. "That’s probably the end of his presidency. Donald Trump has made a promise to the American people. He’s going to secure our border."

Graham also said he hoped that Sen.-elect Mitt RomneyWillard (Mitt) Mitt RomneyCoronavirus and America's economic miracle Former Romney strategist joins anti-Trump Lincoln Project Romney defends Joe Scarborough, staffer's widower: 'Enough already' MORE (R-Utah) and other lawmakers view the dispute over the border wall as "a fight worth having.”

“That’s the end of us if we give in on this issue as Republicans," Graham said. "I hope Mitt Romney and everybody else knows this is a fight worth having."

Romney wrote an op-ed in The Washington Post on Tuesday criticizing Trump's character, saying he hasn't "risen to the mantle" of the presidency. But Romney also said during an interview on CNN on Wednesday that he "would vote for the border wall."

The federal government has been in a partial shutdown since Dec. 22 that was prompted by Trump's demand that a spending bill include $5 billion for a wall along the southern border.

Democrats, who will gain control of the House on Thursday when the new Congress begins, have pledged not to approve any funding for the wall. 

The two sides showed no indications of coming closer to an agreement following a meeting between Trump and lawmakers Wednesday at the White House, with Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellThe Hill's Morning Report - Presented by Facebook - George Floyd's death sparks protests, National Guard activation COVID-19 workplace complaints surge; unions rip administration Senate Democrats pump brakes on new stimulus checks MORE (R-Ky.) suggesting that the shutdown may continue for weeks.

McConnell said later Wednesday that a House plan to fully reopen the federal government is a "total non-starter," comparing it to "political performance art" that will not be taken up in the Senate.

House Democrats are expected to vote on Thursday on a package to reopen the government. One bill would fund the Department of Homeland Security through Feb. 8. The second would fund the remaining six bills through Sept. 30, the end of the 2019 fiscal year.