WASHINGTON – Top Republicans warned the Trump administration Tuesday against imposing new tariffs on all Mexican imports, saying the president risks an embarrassing congressional reversal if he goes through with the plan.

President Donald Trump has threatened to impose 5% tariffs on Mexico starting next week unless the Mexican government stops the flow of migrants coming to the U.S. border. Trump said he would increase the tariffs by 5 percentage points each month and warned they could reach 25% by Oct. 1.

But Senate GOP leaders publicly and privately pressed the White House to negotiate a solution with Mexican officials and said Trump could face a congressional blockade if he goes through with the levies.

“Republicans don’t like taxes on American consumers, which is what tariffs are,” said Sen. Ron Johnson, chairman of the Senate Homeland Security and Governmental Affairs Committee.

“I think the president and the administration ought to be concerned about another vote of disapproval,” said Johnson, R-Wis., referring to a legislative tool lawmakers could use to overturn Trump’s justification for the tariffs.

Secretary of State Mike Pompeo will hold pivotal talks with Mexican officials Wednesday amid the growing political backlash.

Johnson and others vented their frustration over Trump’s tariff threat during a closed-door lunch on Tuesday with several administration officials who were dispatched to the Hill to explain the president's legal basis for the tariffs.

Sen. Ted Cruz, R-Texas, said that Trump administration officials got an earful from lawmakers expressing “deep concern and resistance to imposing tariffs on trade with Mexico because it would hurt American jobs.” He said the current showdown with Mexico is like “a giant game of chicken,” with potentially disastrous economic results.

“It’s like two trucks headed straight at each other on a country road. If the outcome of this is that Mexico blinks, and they turn, and they actually become active, productive partners in helping stop illegal immigration, that would be a good outcome,” Cruz said. “But if the outcome of this game of chicken is massive new tariffs that destroy jobs in Texas, and across the country, that would be a terrible mistake.”

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The Senate's top Democrat, Chuck Schumer of New York, said Trump was probably bluffing – prompting a fierce response from the president.

"Frankly, I don't believe President Trump will actually go through with the tariffs," Schumer said on the Senate floor Tuesday. "President Trump has a habit of talking tough and then retreating because his policy often ... can't be implemented or doesn't make sense."

"Can you imagine Cryin’ Chuck Schumer saying out loud, for all to hear, that I am bluffing with respect to putting Tariffs on Mexico," Trump tweeted Tuesday night. "What a Creep."

Mexican Foreign Minister Marcelo Ebrard and other top officials are in Washington this week, lobbying the Trump administration against imposing the tariffs – saying it will weaken Mexico's ability to address the migration crisis.

Most of the migrants trying to come to the United States are from Central America, not Mexico. They’re fleeing violence, poverty and corruption and other problems in their home countries.

In a news conference on Monday, Ebrard and other Mexican officials noted that their government has already taken major steps toward stemming the flow of migrants, by cracking down on human smuggling and returning more than 80,000 migrants crossing through Mexico to their home countries.

Trump dismissed those efforts Tuesday and seemed to double-down on his tariff threat.

"Millions and millions of people are coming right through Mexico," Trump asserted at a joint news conference in London with British Prime Minister Theresa May. "Mexico should step up and stop this onslaught."

He said Republicans would be "foolish" to try to block the tariffs. But experts said Trump's plan is vulnerable to a congressional override.

"This is such a frontal assault not just on Congress’ constitutional power but really on what has been a core of Republican ideology for now, which is a belief in free trade and low taxes," Edward Alden, a senior fellow at the Council on Foreign Relations, a foreign policy think tank, said during a conference call Tuesday.

Alden said it seems to be "sinking in up on the Hill" that these tariffs could wipe out the economic benefits of the tax cuts that Republicans enacted in 2017.

Shannon K. O'Neil, an expert on Latin America with the council, said Trump's demands that Mexico stop the influx of migrants is unrealistic.

"The challenge for Mexico frankly is that they don’t have the capacity to do this," she said. "This is a problem that the United States admits that they can’t deal with and they expect Mexico, a country with fewer resources and a much less capable bureaucracy, to do that work for them."

It's not clear if Pompeo and Ebrard will be able to find a solution to the stand-off during their meeting on Wednesday. But lawmakers said they were hoping for that outcome so that Congress does not have to step in.

Senate Majority Leader Mitch McConnell, R-Ky., side-stepped reporters' questions Tuesday about what he would do if Trump went through with the tariffs.

"We’re still hoping that this can be avoided," McConnell said after the lunch meeting. "Apparently these talks are going well. Our hope is the tariffs will be avoided."

Cruz was more direct, noting that a 25% tariff would translate into nearly $30 billion in new taxes on his home state of Texas, which imports more than $100 billion in goods from Mexico annually.

“There is no doubt we have an emergency at the border,” Cruz said. “But there is no reason for Texas farmers and ranchers and manufacturers and small businesses to pay the price of massive new taxes.”

Contributing: Deborah Berry

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This article originally appeared on USA TODAY: 'A giant game of chicken': GOP lawmakers warn against Trump's threatened tariffs on Mexico