Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans signal openness to working with Biden Loeffler calls for hearing in wake of Netflix's 'Cuties' Quinnipiac poll shows Graham, Harrison tied in South Carolina Senate race MORE (R-S.C.) on Wednesday cautioned President Trump Donald John TrumpBarr criticizes DOJ in speech declaring all agency power 'is invested in the attorney general' Military leaders asked about using heat ray on protesters outside White House: report Powell warns failure to reach COVID-19 deal could 'scar and damage' economy 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 Romney Willard (Mitt) Mitt RomneyThe Memo: Warning signs flash for Trump on debates GOP votes to authorize subpoenas, depositions in Obama-era probe Overnight Defense: Trump hosts Israel, UAE, Bahrain for historic signing l Air Force reveals it secretly built and flew new fighter jet l Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' 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 McConnell Addison (Mitch) Mitchell McConnellSenate Republicans signal openness to working with Biden Hillicon Valley: DOJ indicts Chinese, Malaysian hackers accused of targeting over 100 organizations | GOP senators raise concerns over Oracle-TikTok deal | QAnon awareness jumps in new poll The Hill's Campaign Report: Biden asks if public can trust vaccine from Trump ahead of Election Day | Oklahoma health officials raised red flags before Trump rally 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.