Republican lawmakers are exhaling with relief after they narrowly dodged a standoff with President Trump Donald John TrumpSteele Dossier sub-source was subject of FBI counterintelligence probe Pelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Trump 'no longer angry' at Romney because of Supreme Court stance MORE this week over tariffs on imports from Mexico.

The fight over immigration and trade had exacerbated tensions between Trump and members of the GOP Senate, risking a major confrontation between the two sides.

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“Very thankful that the president didn’t move ahead with it, very thankful that Mexico is stepping up and doing more to assist us with the humanitarian crisis,” Sen. Joni Ernst Joni Kay ErnstTillis appears to reinforce question about COVID-19 death toll The power of incumbency: How Trump is using the Oval Office to win reelection Poll: Trump opens up 6-point lead over Biden in Iowa MORE (Iowa), a member of the GOP leadership team, said Monday in describing her reaction to Trump’s announcement Friday of a deal.

Senate Commerce Committee Chairman Roger Wicker Roger Frederick WickerHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google Senate panel threatens subpoena for Google, Facebook and Twitter executives MORE (R-Miss.) also described himself as “relieved” and praised Trump for “devising a strategy that’s paid off.”

“I hope we can go ahead and get Speaker [Nancy] Pelosi [(D-Calif.)] to take up USMCA and we can celebrate an astounding victory,” he added, referring to the deal with Canada and Mexico to replace the 1994 North American Free Trade Agreement.

Trump had threatened to impose a 5 percent tariff on all Mexican imports by Monday unless Mexico did more to stop illegal immigration from Central America. He had said the tariffs would rise to 25 percent by October without action.

Trump’s threats had sparked talk among senators about a new disapproval resolution, which some Republicans predicted would have passed.

It’s not entirely clear how the GOP’s distaste for the tariffs and pressure on Trump to relent led to the deal with Mexico. There were significant doubts from members of both parties that when push came to shove, the GOP Senate would really take dramatic action against Trump — especially with opponents of the tariffs almost certain to not have the votes to overturn a Trump veto in the House.

Also unclear is whether Republicans and Trump can avoid future fights on trade, the issue that has consistently pulled them apart.

Sen. John Cornyn John CornynQuinnipiac polls show Trump leading Biden in Texas, deadlocked race in Ohio The 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 MORE (R-Texas) said it will largely depend on whether the deal with Mexico reduces the flow of illegal migrants.

“The real test is whether that 144,000 number from May, whether it goes down. That will be the best evidence,” he said, citing the number of migrants taken into custody by U.S. Customs and Border Protection last month, a 32 percent increase compared with April.

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Ernst said it will depend on whether Mexico sticks to its pledges. She warned that the tariff threat isn’t entirely off the table and could come back if the border situation fails to improve.

“If Mexico does not step up, I think the president will come back to it,” she said.

Republican lawmakers say it’s time for Congress to act by providing more money to deal with the surge of migrants from Central America and to reform asylum laws, which have contributed to overflowing detention facilities and a growing humanitarian crisis.

“We need to keep moving. That’s on us, too, to make sure that we’re funding border security technology, physical barriers, additional agents, additional beds that are necessary. We’ve got to find a way to come together on that and right now we’re at a stalemate,” said Ernst, a member of the Judiciary Committee, which has jurisdiction over the issue.

A senior Senate Republican aide said the upcoming July 4 recess could provide a useful target date for passing the $4.5 billion in emergency funding the White House requested last month to deal with the border crisis.

That funding bill could be paired with immigration reforms that are being pushed by Senate Judiciary Committee Chairman Lindsey Graham Lindsey Olin GrahamSteele Dossier sub-source was subject of FBI counterintelligence probe Hillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google MORE (S.C.) and Cornyn, a member of the GOP leadership team.

The Judiciary Committee will hold a hearing Tuesday with acting Secretary of Homeland Security Kevin McAleenan on Graham’s proposal to require Central American migrants to apply for asylum from their home countries or from Mexico; hire more immigration judges; and extend the time that children can stay in detention with their families while their asylum claims are processed.

Cornyn is pushing a bill co-sponsored by Democratic Rep. Henry Cuellar (Texas) that would reform procedures for migrant families detained at the border and increase resources at U.S. ports of entry.

Democratic leaders, however, are reluctant to give Trump a victory on his signature issue: illegal immigration. And high-profile efforts to negotiate a bipartisan immigration deal have already failed since Trump took office.

Democrats rejected adding the $4.5 billion border supplemental spending bill to a disaster relief package that passed the Senate before the Memorial Day recess.

Nevertheless, there is growing pressure on Democrats to reach a deal with Republicans.

The New York Times on Sunday published an editorial urging Congress “to cut the squabbling and pass an emergency relief package.”

Trump on Monday blasted Democrats as obstructionist and lacking a plan for the border.

“In fact, the Democrats are doing NOTHING, they want Open Borders, which means Illigal Immigration, Drugs and Crime,” he tweeted.

That prompted Senate Minority Leader Charles Schumer Chuck SchumerPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' 3 reasons why Biden is misreading the politics of court packing Cruz blocks amended resolution honoring Ginsburg over language about her dying wish MORE (D-N.Y.) to come to the Senate floor on Monday afternoon to dispute what he called “another bogus claim.”

Schumer insisted that Democrats have a border plan that “would be far more effective at dealing with the actual problem than what President Trump announced on Friday.”

He called for allowing would-be migrants to apply for asylum from their own countries; the United States to provide security assistance to Central American countries to crack down on violent gangs, drug cartels and human traffickers; and to fund an increase of immigration judges at the border so that migrants wouldn’t have to wait so long for their claims to be processed.

Creating a path for migrants to apply for asylum from their own countries and increasing the number of immigration judges are two areas of common ground with Graham’s bill and could provide the starting point for bipartisan negotiations.

Sen. Deb Fischer Debra (Deb) Strobel FischerHillicon Valley: Election officials prepare for new Russian interference battle | 'Markeyverse' of online fans helps take down a Kennedy | GOP senators unveil bill to update tech liability protections Google, Apple, eBay to meet virtually with lawmakers for tech group's annual fly-in Congress botched the CFPB's leadership — here's how to fix it MORE (Neb.), a member of the Senate GOP leadership team, acknowledged Monday that the economic impact of Trump’s threatened tariffs “would have been a challenge to face.”

She said it’s now up to Congress to pass border security and immigration legislation to take the threat of tariffs away completely.

“Congress needs to step up and do its job and provide funding to address a humanitarian crisis and also address the security of this country,” she said.

Asked about the prospect of Democrats agreeing to anything that could get Trump’s signature, Fischer said “I hope they would.”

“I look forward to working with them,” she said.