Senator John Cornyn (R-TX), the Senate’s second-ranking Republican, said there is little chance Congress will block President Donald Trump’s tariffs on aluminum and steel, but lawmakers who support free trade will keep lobbying the administration to add more exemptions, according to a Bloomberg report.

Senator Cornyn said Monday that Trump already has responded to lawmakers urging that he curtail the impact of the tariffs and that is probably the approach most likely to have an impact. The administration is still working out exemptions, including for Canada and Mexico, from the tariffs of 25 percent on steel imports and 10 percent on aluminum before they take effect later this month.

“We’re making progress without legislation,” Cornyn told reporters. Cornyn chairs the Senate Finance subcommittee on international trade. “The president carving out states that aren’t hostile actors when it comes to trade is a positive development, and I expect we’ll continue that conversation.”

Cornyn’s remarks are among the first public acknowledgments from Republicans in Congress that they will not go to battle with Trump over the tariffs, even though it veers from the party’s decades-long support for free trade. Business groups that are longtime GOP allies, including the Business Roundtable and the U.S. Chamber of Commerce, are opposed to the tariffs.

House Republicans also say they will work with the White House, rather than introducing legislation to curb the President’s authority over trade. A veto-proof majority is a high bar for an issue where some Democrats support more protectionist measures and some Republicans would hesitate to oppose President.

Congress “will continue to be actively engaged with the administration to preserve the strong economic momentum from last year’s tax cut,” Ways and Means Chairman Kevin Brady (R-TX) said in a statement.

The low-key response from top Republicans comes the same day that Senator Jeff Flake (R-AZ)  introduced legislation that would nullify the levies on metals imports. Flake says Trump’s plan can’t be modified. “If you modify it, all you’re doing is creating more uncertainty, giving the president abilities to be flexible on tariffs, to wake up one day and say we’re exempting Australia but not Brazil” he said.

Senator Mike Lee (R-UT) is pushing a measure that would allow most future tariffs to come under congressional review.

Cornyn on Friday said the administration also may face legal challenges over the tariffs at the World Trade Organization and in U.S. courts. Legal experts have cast doubt that cases brought in U.S. courts would succeed.

White House press secretary Sarah Huckabee Sanders on Monday dismissed a question about Congress blocking or delaying the tariffs. “The president’s been clear for quite some time what his position is and what his authority is,” she said.