Republican senators warned Tuesday that President Donald Trump doesn't have the political backing to impose tariffs on Mexican goods, and that they could deal him an embarrassing rebuke if he moves forward with the levies.

“I think the administration ought to be concerned about another vote of disapproval on another national emergency act, this time about trying to implement tariffs,” Sen. Ron Johnson, R-Wis., said after a policy lunch attended by GOP senators and Trump administration lawyers.

Trump, however, said Tuesday that the GOP would be "foolish" to try to block his plan.

"I don't think they will do that," Trump said during a news conference with British Prime Minister Theresa May in London. "I think if they do, it's foolish."

The president has vowed to apply tariffs of 5 percent on all Mexican goods next week and increase the rate to 25 percent in coming months if Mexico does not substantially halt illegal immigration across the U.S.-Mexican border, which is at a decade high this year.

Asked if Mexico, which has recently stepped up border apprehensions and deportations of Central American migrants, was doing enough to stave off tariffs, Trump said Tuesday that "it's more likely that the tariffs go on" than not.

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More than half a dozen Republican senators raised concerns about the tariffs or asked questions of a pair of administration lawyers at the Tuesday lunch meeting, according to multiple sources, as well as a senator who attended.

Johnson said he told the lawyers to pass on the message that there is a good chance Congress would defeat any attempt to impose the tariffs by voting to disapprove of the action, suggesting Congress would be able to override a presidential veto.

Senate Majority Leader Mitch McConnell on Tuesday afternoon acknowledged his party's opposition to Trump's plan.

"There is not much support in my conference for tariffs, that's for sure," he said.

Asked if he would try to block the tariffs, the Kentucky Republican noted the administration's talks with Mexican officials this week on tariffs and immigration and said "our hope is that the tariffs will be avoided and we'll not have to answer any hypotheticals such as you suggest."

A move to block Trump's tariffs on Mexico, which are set to go into effect June 10, would be one of the most significant repudiations of the president by his own party to date. With the help of 12 Republican senators, Congress passed a resolution of disapproval in March to override Trump's use of his national emergency declaration to reapportion billions of dollars for his border wall, which Trump vetoed.

If enough Republicans supported another resolution of disapproval because of their frustration over Trump's planned tariffs, it would undermine both the tariffs and the president's border wall funding. At least 20 Republican senators would be needed to override a presidential veto, assuming all Democrats and the two independents who caucus with them supported the move.

Senate Majority Whip John Thune, R- S.D., said earlier Tuesday that a resolution of disapproval would probably gain more support from GOP lawmakers this time, but members were trying to understand what authority the president was using, the goal of the tariffs and the actions Mexico would need to take to have them lifted.

"There’s a lot of questions about it," Thune said. "But I mean, suffice it to say, our members have a lot of concerns. They are very concerned about it."

Republican lawmakers and the business community are worried that the White House hasn't fully thought through the possible economic consequences of the proposed tariffs, two Republican Senate sources told NBC News. Some lawmakers are also concerned about the White House's lack of messaging, planning and forethought on the tariffs, the sources said.

After Trump announced the tariffs, Sen. Pat Toomey, R-Pa., said in a statement that the president "is right to point out the crisis at our southern border. However, a blanket tax increase on everything Americans purchase from Mexico is the wrong remedy."

"Tariffs are a dangerous and risky economic tool," Toomey said. "They raise the cost of products for American families, reduce market share abroad for U.S. exporters, and make our economy less competitive globally. History has shown us time and again that nobody wins a trade war: Trade is mutually beneficial, and trade restrictions, like tariffs, are mutually harmful."

United States-Mexico-Canada Agreement concerns

House Speaker Nancy Pelosi said Tuesday that Trump's planned tariffs could also jeopardize the ratification of the trade deal between the U.S., Mexico and Canada, which the leaders of the three countries signed in November.

“This has really thrown an apple of discord into it," Pelosi, D-Calif., told NBC News, adding that Republicans "really got to separate themselves from the president on this because it’s so detrimental."

Some Republican senators also expressed concern Tuesday about the impact of tariffs on congressional efforts to approve the trade deal.

"We need to separate the issues," Sen. Joni Ernst, R-Iowa, said. "One, for Iowa, it is important we get the trade deals done. So USMCA needs to take priority and then talk about other options other than tariffs would be my want, my thought, my desire. If we can dissuade the president I’d like to do that.”

Sen. Shelley Moore Capito, R-W.Va., also said she was against the tariffs.

"We don’t agree with tariffs as a strategy, but in this particular case, I think it further muddles the water because we had real momentum here, and I think many colleagues are saying the tariffs have to come off before we can look at the trade deals," she said.

The Trump administration kicked off the congressional approval process for the trade deal last week despite House Democrats' lingering concerns about the effects of the agreement, prompting Pelosi to say in a statement that the move was "not a positive step“ and indicated "a lack of knowledge on the part of the administration on the policy and process to pass a trade agreement."

Global equities tumbled after Trump's unexpected threat last week of tariffs against the United States' biggest trade partner, as investors feared his aggressive trade diplomacy could tip the United States and other major economies into recession.

To head off the punitive tariffs, a senior Mexican delegation began high-level talks Monday in Washington, where it was expected to be pushed to do more to hold back Central American migrants.

Trump on Sunday called Mexico an "abuser" of the United States and said he wanted action, not talk. Mexico has signaled it would retaliate to the tariffs, with targets likely to include farm products on Trump supporting states.