Senate Republicans say 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 should postpone tariffs set to be imposed on Mexican exports Monday, and allow more time for negotiators to reach a deal.

The senators say further negotiations could help prevent an escalating trade fight they say would damage the U.S. economy.

“We have a lot of people who don’t want to see this go into effect next week,” said Senate Republican 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 (S.D.).

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Vice President Pence and Secretary of State Mike Pompeo Michael (Mike) Richard PompeoTreasury sanctions individuals, groups tied to Russian malign influence activities Navalny released from hospital after suspected poisoning Overnight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers MORE met with a Mexican delegation on Wednesday for about 90 minutes but failed to reach a deal that involved curbing illegal immigration to the United States.

Trump said on Twitter the talks would resume Thursday, and vowed that if there were no deal, the tariffs would be imposed on schedule.

“Progress is being made, but not nearly enough!” wrote Trump, who then noted a report issued by his administration earlier Wednesday that said border arrests in May had hit a record 133,000.

The results appeared to have been released on Friday to put added pressure on Mexico.

Trump said talks would resume “with the understanding that, if no agreement is reached, Tariffs at the 5% level will begin on Monday, with monthly increases as per schedule. The higher the Tariffs go, the higher the number of companies that will move back to the USA!”

Mexican Foreign Minister Marcelo Ebrard offered a hopeful note while speaking to reporters after the talks ended.

“Both sides recognized that the current situation cannot be maintained as it is,” he said, referring to May’s record border crossings.

Trump is facing stiff opposition from Senate Republicans over the tariffs, though it is uncertain if the GOP will actually challenge him.

House Minority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy threatens motion to oust Pelosi if she moves forward with impeachment Kate Schroder in Ohio among Democratic challengers squelching GOP hopes for the House McCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother MORE (R-Calif.) offered support for Trump’s tariffs on Wednesday and warned Republicans against undercutting the administration’s ability to negotiate with Mexico.

Speaker Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE (D-Calif.) criticized Trump’s plan, saying he is treating a neighboring country like “an enemy.”

But she also suggested that even if the House and Senate passed a resolution disapproving of the tariffs, it was unlikely the House could override a presidential veto.

“The Republican leader said they’re going to stick with the president on this,” Pelosi said, referring to McCarthy. “I don’t know how many of his members go along with that. I think the Senate probably has the votes to override.”

Whether the Senate would want to go that far is unclear.

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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.), who is up for reelection himself next year, has generally sought to avoid confrontations with Trump, and Republicans who stand against the president are likely to attract primary challengers.

Trump on Tuesday said it would be “foolish” for GOP lawmakers to try to stop the tariffs, and some Republican senators on Wednesday downplayed the possibility of overriding a presidential veto.

Senate Homeland Security Committee Chairman 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 (R-Wis.), who warned administration officials Tuesday that the Senate would vote on a disapproval resolution, changed his tone on Wednesday.

He said he informed Mexican Ambassador Martha Bárcena Coqui earlier in the day that Republicans would not vote to block Trump’s tariffs.

“I talked to the Mexican ambassador. I wanted to make sure that she realized that if the president decides to invoke tariffs, I don’t think there’s a possibility for a veto override,” Johnson told reporters after the call.

Thune said McConnell is “talking to the White House,” and 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, said he thinks the tariffs should be postponed. Cornyn said he’s hearing a lot of pushback from constituents in Texas who are worried about the economic impact.

“It would hurt the economy not just in Texas, but Mexico is one of our major export countries and it would hurt, I think, the entire U.S. economy,” he said.

Texas exported $109.7 billion in goods to Mexico in 2018, about 35 percent of the state’s total exports, according to the Office of the U.S. Trade Representative.

At a closed-door meeting on Tuesday, Republicans hammered administration officials, arguing the tariffs would boomerang on the United States. The tariffs, if they go into place on Monday, are set to rise by 5 percentage points each month before topping out at 25 percent in October.

“There was a lot of interest yesterday in [there being] no precipitous actions on the tariffs,” said Senate Republican Policy Committee Chairman Roy Blunt Roy Dean BluntSocial media platforms put muscle into National Voter Registration Day Senate GOP faces pivotal moment on pick for Supreme Court This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (R-Mo.), summarizing the discussion.

Senate Republicans want a chance to meet with Trump after he returns from Europe on Friday to make their case on the need to delay tariffs.

“I think there’s going to be a group of senators who are going to see the president to express some concerns about what the impact would be on the USMCA, for example, and we’ll see what happens from there,” said Sen. Susan Collins Susan Margaret CollinsClub for Growth to spend million in ads for Trump Supreme Court nominee Maryland's GOP governor says Republicans shouldn't rush SCOTUS vote before election The Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November MORE (R-Maine), referring to the new trade deal that will replace the North American Free Trade Agreement if it is ratified.

Trump has made passing legislation to implement the USMCA a top priority for 2019. The president and his senior economic adviser, Larry Kudlow Larry KudlowMORE, pressed Democratic leaders about ratifying the new deal when they met in late April to discuss a possible infrastructure package.

There was one notable sign that the pressure on the administration was having some effect.

Senior White House trade adviser Peter Navarro told CNN on Wednesday that tariffs against Mexico “may not have to go into effect” if it can show progress in slowing the flow of migrants from Central America into the United States.

“We believe that these tariffs may not have to go into effect precisely because we have the Mexicans’ attention,” he said.

Rafael Bernal and Jordan Fabian contributed.