Corker and other Republicans have pushed back against Trump only sparingly since he took office in January 2017. But a consistent point of concern from free trade GOP lawmakers is Trump's push to impose tariffs and crack down on trade practices that he says sap American jobs.

It is unclear whether a veto-proof, two-thirds majority in both chambers of Congress would back the measure. Numerous Republicans and Democrats have backed Trump's push to crack down on alleged trade abuses, and some GOP lawmakers in pro-Trump states may hesitate as they risk drawing the president's ire. House Speaker Paul Ryan has questioned whether the legislation could get through Congress.

Trump called Corker to urge him to abandon the plan Wednesday morning. The Tennessee Republican said earlier that he told the president that he plans to go through with his legislation.

Corker's bill, co-sponsored by five other Republican and four Democratic senators, would require congressional approval for tariffs levied for national security reasons. The Trump administration used a national security justification when putting steep tariffs on steel and aluminum imports from key U.S. allies, prompting fears about a trade war and deteriorating relations with foreign countries.

The most outrage in response to the president's trade actions came last week, when Trump said he would not exempt Canada, Mexico and the European Union from stiff tariffs of 25 percent and 10 percent on steel and aluminum imports, respectively. Those entities quickly responded with retaliatory measures and harsh rebukes of Trump's policy.

Corker is among the Republicans trying to head off escalating trade conflicts that could potentially harm the U.S. economy. He has questioned the Trump administration's justification that it imposed the tariffs because of national security risks.

Republican Sens. Pat Toomey of Pennsylvania, Lamar Alexander of Tennessee, Ron Johnson of Wisconsin, Mike Lee of Utah and Jeff Flake of Arizona joined Corker and supporting the bill. On the Democratic side, Sens. Heidi Heitkamp of North Dakota, Mark Warner of Virginia, Brian Schatz of Hawaii, and Chris Van Hollen of Maryland co-sponsored it.

Senate Majority Leader Mitch McConnell said Tuesday that he would not take up Corker's tariff bill as separate legislation. However, he would be open to adding it as an amendment to other legislation such as the National Defense Authorization Act.

After Corker unveiled the legislation, McConnell called it an "exercise in futility" on Wednesday night.

Ryan on Wednesday downplayed the chances of the bill getting through the House and past Trump's possible veto. He told reporters that "you can do the math on that."

Congress can override a president's veto with a two-thirds vote in each chamber. However, it is unclear if many Republicans representing states in which Trump is popular would want to go against the president's wishes. Numerous Democrats in states with heavy manufacturing presences have also supported Trump's trade policy.

Trump's tariff moves have set conservative interest groups against him. The Koch political network, for instance, said it would spend millions of dollars to oppose the measures. Both the U.S. Chamber of Commerce and Koch Industries endorsed Corker's legislation.

The tariffs also have political stakes for November's midterm elections, as regions in which candidates are running can drive their views on the measures. The Democrat running for the retiring Corker's seat — former Tennessee Gov. Phil Bredesen — has criticized the tariff actions.

"They will drive up prices, hurt our economy and will cost jobs, especially in our important automotive sector," he said in a statement Wednesday. "The retaliatory tariffs that are promised to follow will hurt our exports, damaging farmers and even hitting iconic Tennessee businesses like Jack Daniel's."

Republican candidate Rep. Marsha Blackburn, who has tied herself closely to Trump in the race, has said she worries the tariffs could lead to a "bad deal for Tennessee," according to Tennessean.com.