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

Sen. Lindsey GrahamLindsey Olin GrahamTrump fires back at Graham over Iran criticism Overnight Defense: GOP wary of action on Iran | Pence says US 'locked and loaded' to defend allies | Iran's leader rules out talks with US Republicans wary of US action on Iran MORE (R-S.C.) on Wednesday cautioned President TrumpDonald John TrumpJimmy Carter: 'I hope there's an age limit' on presidency White House fires DHS general counsel: report Trump to cap California trip with visit to the border 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 RomneyLobbying World Republicans wary of US action on Iran The Hill's Morning Report - Trump takes 2020 roadshow to New Mexico 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 McConnellDemocrats seize Senate floor to protest gun inaction: 'Put up or shut up' Democrats press for action on election security Hillicon Valley: Election security looms over funding talks | Antitrust enforcers in turf war | Facebook details new oversight board | Apple fights EU tax bill 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.