President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE moved closer Tuesday to an explosive confrontation with his own party over trade and immigration, two of the signature issues of his presidency.

GOP senators offered White House officials a stern warning behind closed doors that the president should not move forward with his plan to impose tariffs on all Mexican imports starting Monday unless that country takes significant steps to curb illegal immigration.

Trump, for his part, all but dared the GOP to try to stop him, saying at a press conference in London that he expected the tariffs to go into place as planned and that it would be “foolish” for Republicans to try to stop them.

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In public, Senate GOP leaders suggested cooler heads would prevail and that a public battle would be avoided. Asked about the possibility of the Senate voting to block Trump’s tariffs, Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) told reporters, “we’re hoping that doesn’t happen.”

But behind the scenes, Republicans including Sens. Rob Portman Robert (Rob) Jones PortmanMcConnell locks down key GOP votes in Supreme Court fight Romney undecided on authorizing subpoenas for GOP Obama-era probes Congress needs to prioritize government digital service delivery MORE (Ohio), Ron Johnson Ronald (Ron) Harold JohnsonThe Hill's 12:30 Report: Ginsburg lies in repose CHC leaders urge Senate to oppose Chad Wolf nomination Top GOP senators say Hunter Biden's work 'cast a shadow' over Obama Ukraine policy MORE (Wis.), Ted Cruz Rafael (Ted) Edward CruzCruz blocks amended resolution honoring Ginsburg over language about her dying wish Trump argues full Supreme Court needed to settle potential election disputes Press: Notorious RBG vs Notorious GOP MORE (Texas) and Cory Gardner Cory Scott GardnerCook Political Report shifts Colorado Senate race toward Democrat Overnight Health Care: US coronavirus deaths hit 200,000 | Ginsburg's death puts future of ObamaCare at risk | Federal panel delays vote on initial COVID-19 vaccine distribution The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting MORE (Colo.) spoke out against the tariffs during a closed caucus meeting attended by White House deputy counsel Patrick Philbin and Department of Justice officials.

After the doors opened, Cruz told reporters “there was deep concern expressed in the lunch about the prospects of tariffs with Mexico.”

Another GOP senator who attended the meeting and requested anonymity to speak candidly said: “I think it's fair to say … that every senator who spoke, and there were probably a half-dozen, generally had the same point of view. Nobody was supportive, who spoke.”

The lawmaker said White House officials were warned that the Senate could block the tariffs with a disapproval resolution, noting that 12 Republican senators voted in March to disapprove of Trump’s use of a national emergency declaration to shift Defense Department funds to construction of a border wall.

Whether Republicans are really willing to go that far remains an open question.

Trump vetoed the disapproval resolution the Senate passed earlier this year, and no one knows whether there would be enough GOP votes to override a second veto.

Trump has said the tariff on Mexico will rise gradually to a maximum of 25 percent by October unless Mexico takes steps to curb illegal immigration. The threat has unsettled the business community and led to fears the U.S.-Mexico supply chain could be deeply disturbed.

Some GOP senators say this time could be different.

Johnson said he personally told administration officials at Tuesday’s lunch meeting that they should be “concerned” about a resolution of disapproval vote.

He voted against a resolution disapproving of Trump’s use of a national emergency declaration to shift around appropriated funds but could support a resolution disapproving of new tariffs based on emergency authority.

“This would be a different vote,” he said. “This would certainly give me great pause in terms of supporting that type of declaration to enact tariffs versus building the wall, which I completely supported.”

“Listen, Republicans don't like taxes on American consumers, what tariffs are,” Johnson added.

Asked if administration officials got the message, he said, "I hope so."

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Sen. Kevin Cramer Kevin John CramerMomentum growing among Republicans for Supreme Court vote before Election Day On Paycheck Protection Program, streamlined forgiveness is key McConnell shores up GOP support for coronavirus package MORE (R-N.D.) predicted at least 20 Republicans would vote for a disapproval resolution rejecting new tariffs against Mexico, which would likely give Trump’s critics the 67 votes they need to override a veto.

Cramer voted against the previous disapproval resolution the Senate passed on March 14.

Senate Majority Whip John Thune John Randolph ThuneOvernight Defense: Stopgap spending measure awaits Senate vote | Trump nominates former Nunes aide for intelligence community watchdog | Trump extends ban on racial discrimination training to contractors, military Remote work poses state tax challenges Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.D.) said it would be tougher to sustain Trump’s veto of a resolution disapproving of his use of emergency power to invoke tariffs.

“The one before was clearly about the border and funding for the border. This is clearly about what a lot of our members view as a tariff, a tax,” he said. “If that vote were to ever occur, I think you’d have a lot more of our members be opposed [to Trump’s emergency declaration] than what you saw last time.”

At the same time, Thune acknowledged later in the day that sustaining a veto of a second disapproval resolution would be a “hard sell” with GOP senators.

Other Republicans expressed doubt that a disapproval resolution will actually come to the floor.

Sen. Mitt Romney Willard (Mitt) Mitt RomneyBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power The Memo: Trump's strengths complicate election picture MORE (R-Utah), a frequent Trump critic, said the president’s tariff threat is a negotiating tactic and won’t result in new levies.

“I believe the president is describing tariffs on Mexico as a way to capture their attention and to get them to take some action to help reduce the flow of illegal immigrants into the country,” he said.

A delegation from Mexico is in Washington this week trying to get a last-minute deal to prevent the tariffs.

Thune said “this could all be avoided if they cut a deal,” referring to the talks with the Mexican delegation.

Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas), an adviser to McConnell, also said he hoped to avoid a vote on a disapproval resolution.

“I’m hopeful that the negotiations with the Mexican delegation will produce a positive outcome. That would be the better way to go as far as I’m concerned,” he said.

McConnell has generally sought to avoid confrontations with Trump, though the president was forced into his first two vetoes earlier this year.

After the lunch, McConnell told reporters “there is not much support in my conference for tariffs, that’s for sure.”

“I think it’s safe to say — you’ve talked to all of our members, we’re not fans of tariffs,” he added.

GOP lawmakers say Trump’s novel use of the International Emergency Economic Powers Act of 1977 and the lack of a precedent has left many questions about whether a disapproval resolution would even come to the Senate floor.

Some argue that Trump’s emergency declaration for the border made in February is still in effect and that another effort to terminate it would have to wait until six months elapsed after Congress’s last effort to pass a disapproval resolution.

“I don’t believe at this point anybody knows for sure until there’s actually something formally submitted what would be required up here and whether it would necessitate a vote or anything like that,” Thune said.

But Senate Minority Leader Charles Schumer Chuck SchumerCruz blocks amended resolution honoring Ginsburg over language about her dying wish Senate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' MORE (D-N.Y.) argued Tuesday afternoon that a second disapproval resolution cannot be avoided.

“I believe there would be a disapproval resolution whether the president uses the previous emergency declaration or a new emergency declaration,” he said. “It’s quite clear that any member of the House and Senate could get on the floor, I think it’s within 15 days, and ask for disapproval.”

Jordan Fabian contributed.