Vice President Mike Pence met with Mexican diplomats Wednesday in an attempt to avert tariffs President Donald Trump has threatened in retaliation to what he sees as Mexican laxity in curbing migrants through the country and into the United States.

At the same time, there is growing concern among Senate Republicans that the president continues to press tariffs on two of the nation’s three largest trading partners. Trump said he believes Mexico wants to avert a new trade war, one that may push the second largest economy in Latin America into recession.

“Mexico can stop it. They have to stop it, otherwise we just won’t be able to do business. It’s a very simple thing. And I think they will stop it. I think they want to do something. I think they want to make a deal, and they sent their top people to try and do it,” Trump said from Ireland while on a five-day European tour to commemorate the 75th Anniversary of the Allied D-Day Invasion of Normandy during World War II.

Senate Republicans during a GOP lunch on Tuesday made clear they have more support for a resolution of disapproval to the national emergency Trump has called in order to implement the tariffs. In March, a dozen Republicans voted against Trump’s use of emergency powers to seize funds for his border wall.

Frustrated by the lack of movement on his signature campaign issue to stem illegal immigration by erecting a wall at the U.S.-Mexican border, Trump told Mexico last week to take a harder line in stopping the flow of immigrants to the border or face a 5% tariff on all its exports to the U.S., effective June 10. The tariffs will escalate to as high as 25% by October if the president is not satisfied with progress.

More than 132,000 people crossing from Mexico were apprehended by U.S. border officers in May, the highest total in more than a decade, the Trump administration said Wednesday.

What measures the president expects Mexico to take are unclear, and Mexican President Andres Manuel Lopez Obrador has said his country is doing all that it can without violating “human rights.” He said he was optimistic regarding the outcome of talks Wednesday, in which Secretary of State Mike Pompeo and U.S. trade representative Robert Lighthizer were expected to attend with Pence and Mexican officials.

John Thune, the No. 2 Senate Republican told reporters, “We have conveyed our concerns to the administration. There are a good number of Republican senators who have expressed both publicly and privately to the White House their concerns about this.”

Some Republicans have said they will not support tariffs and may consider legislation to prevent Trump from imposing them unilaterally in the future.

Sen. Ron Johnson, R-Wis., said a presidential attempt to impose tariffs on Mexico by declaring an immigration emergency “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.”

He added, “Listen, Republicans don’t like taxes on American consumers, [that's] what tariffs are.”

Peter Navarro, a Trump trade advisor, said he was optimistic the tariffs would not be imposed given Mexican cooperation.

"We believe that these tariffs may not have to go into effect precisely because we have the Mexicans' attention," Navarro said.