Senators are moving forward with legislation that would curb President TrumpDonald John TrumpDem lawmaker says Electoral College was 'conceived' as way to perpetuate slavery Stanley Cup champion Washington Capitals to visit White House on Monday Transportation Dept requests formal audit of Boeing 737 Max certification MORE's authority on tariffs, despite opposition from the White House.

"If the president truly believes invoking Section 232 is necessary to protect the United States from a genuine threat, he should make the case to Congress and to the American people and do the hard work necessary to secure congressional approval," Sen. Bob CorkerRobert (Bob) Phillips CorkerTrump keeps tight grip on GOP Brexit and exit: A transatlantic comparison Sasse’s jabs at Trump spark talk of primary challenger MORE (R-Tenn.) said in a statement announcing the bill.

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In addition to Corker, Sens. Heidi HeitkampMary (Heidi) Kathryn HeitkampAnnual scorecard ranks GOP environmental efforts far below Dems in 2018 Overnight Energy: Trump taps ex-oil lobbyist Bernhardt to lead Interior | Bernhardt slams Obama officials for agency's ethics issues | Head of major green group steps down Trump picks ex-oil lobbyist David Bernhardt for Interior secretary MORE (D-N.D.), Pat ToomeyPatrick (Pat) Joseph ToomeyOvernight Defense: Pick for South Korean envoy splits with Trump on nuclear threat | McCain blasts move to suspend Korean military exercises | White House defends Trump salute of North Korean general WH backpedals on Trump's 'due process' remark on guns Top GOP candidate drops out of Ohio Senate race MORE (R-Pa.), Mark WarnerMark Robert WarnerDems request probe into spa owner suspected of trying to sell access to Trump Live video of New Zealand shooting puts tech on defensive The Hill's Morning Report — Trump readies first veto after latest clash with Senate GOP MORE (D-Va.), Lamar AlexanderAndrew (Lamar) Lamar AlexanderWhite House proposes limits on student loan borrowing as part of higher education reforms The 25 Republicans who defied Trump on emergency declaration Trump issues first veto, warning of 'reckless' resolution MORE (R-Tenn.), Brian SchatzBrian Emanuel Schatz Advocate says Trump administration's new proposal would do 'absolutely nothing' to alleviate student debt Hillicon Valley: Huawei official asks US to ease restrictions | Facebook loses top execs | Defense officials hit Google over China | Pro-Trump 'safe space' app pulled over security flaw | Senators offer bill on facial recognition technology Senators introduce bill to regulate facial recognition technology MORE (D-Hawaii), Ron JohnsonRonald (Ron) Harold JohnsonScott Walker considering running for Wisconsin governor or Senate: report GOP moves to rein in president's emergency powers The Hill's 12:30 Report: O'Rourke jumps into 2020 fray MORE (R-Wis.), Chris Van HollenChristopher (Chris) Van HollenThe Hill's 12:30 Report: Manafort sentenced to total of 7.5 years in prison Hillicon Valley: Google takes heat at privacy hearing | 2020 Dems to debate 'monopoly power' | GOP rips net neutrality bill | Warren throws down gauntlet over big tech | New scrutiny for Trump over AT&T merger Trump faces new scrutiny over AT&T-Time Warner merger MORE (D-Md.), Mike LeeMichael (Mike) Shumway LeeThe Hill's 12:30 Report: Trump hits media over New Zealand coverage GOP moves to rein in president's emergency powers The 25 Republicans who defied Trump on emergency declaration MORE (R-Utah), Jeff FlakeJeffrey (Jeff) Lane FlakeTrump keeps tight grip on GOP McSally to back Trump on emergency declaration Flake: Biden 'strikes fear in a lot of Republicans' MORE (R-Ariz.), Ben SasseBenjamin (Ben) Eric SasseRepublicans up for reelection fear daylight with Trump 12 Republican senators defy Trump on emergency declaration  Trump faces growing Senate GOP backlash on emergency declaration MORE (R-Neb.) and Johnny IsaksonJohn (Johnny) Hardy IsaksonThe Hill's 12:30 Report: O'Rourke jumps into 2020 fray Trump vows veto ahead of Senate vote on emergency declaration Senate to rebuke Trump on wall MORE (R-Ga.) are supporting the bill.

"There is no real national security threat that these tariffs are a response to. They are an effort to impose a protectionist policy for economic purposes," Toomey said in a floor speech blasting the administration's decisions.

The bill would require Trump to submit tariffs implemented under Section 232 of the trade law for approval to Congress. Any approval legislation would then be fast-tracked through both chambers.

Senators are introducing the legislation despite receiving pushback from Trump, who earlier on Wednesday privately urged Corker not to file his bill.

“I talked at length with the president about it today. He's obviously not pleased with this effort,” Corker separately told reporters.

Corker added that Trump's main message in the phone call, which the president initiated, was for Corker to not move forward with the proposal.

But congressional Republicans are becoming increasingly frustrated with Trump's trade policy, which they worry could roil the economy just months before a midterm election. 

The administration ratcheted up long-simmering tensions late last week when they announced that they would subject steel and aluminum imports from Canada, Mexico and the European Union to steep tariffs, ending an exemption for the trading allies.

A group of GOP senators met with Trump on Wednesday at the White House to discuss trade. The meeting was organized by GOP Sen. Lindsey GrahamLindsey Olin GrahamGraham: Dems want to abolish Electoral College because they 'want rural America to go away' Overwhelming majority of voters want final Mueller report released: poll Bottom Line MORE (S.C.).

“I think Sen. Graham, who is the leader of that meeting, just wants to talk to the president about his end game,” Sen. John CornynJohn CornynGOP rep to introduce constitutional amendment to limit Supreme Court seats to 9 Court-packing becomes new litmus test on left Cornyn shrugs off Trump criticism of 'SNL' MORE (R-Texas) told reporters when asked about the meeting.

Graham said after the closed-door meeting that Trump is "on track to get us better trade deals" and signaled he will oppose Corker's legislation.

“Now is not the time to undercut President Trump’s ability to negotiate better trade deals. I will not support any efforts that weaken his position," Graham said in a statement.

Notably missing from the supporters of Corker's bill are members of Senate GOP leadership.

Some GOP senators are wary of picking a fight with Trump, saying lawmakers should focus on trying to change the president’s mind. 

"I'm not sure right at this particular time it's advisable. ... My preference would be to convince the president that perhaps he should take a different approach," Sen. Pat RobertsCharles (Pat) Patrick RobertsPompeo jokes he'll be secretary of State until Trump 'tweets me out of office' Senators offer bipartisan bill to fix 'retail glitch' in GOP tax law Kansas Senate race splits wide open without Pompeo MORE (R-Kan.) told reporters. 

Pressed if that strategy was working, Roberts acknowledged, "to date, no." 

Sen. John KennedyJohn Neely KennedyMORE (R-La.) added that while he is reviewing Corker's legislation, he still believes "that the president is too smart to start a trade war." 

Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellGOP rep to introduce constitutional amendment to limit Supreme Court seats to 9 The Hill's Morning Report - Dems contemplate big election and court reforms Court-packing becomes new litmus test on left MORE (R-Ky.) told reporters on Tuesday that he would not bring up the tariff legislation as a stand-alone bill but noted the National Defense Authorization Act (NDAA) was open to amendment.

“I'm not going to call it up free-standing. You're suggesting it might be offered as an amendment. NDAA's going to be opened, we'll see what amendments are offered,” McConnell said, asked about Corker's bill.

Corker has pointed to the NDAA as one potential vehicle for his tariff legislation. But getting the bill brought up as an amendment to the defense policy bill would require the consent of every senator.

Sen. James InhofeJames (Jim) Mountain InhofeThe Hill's Morning Report - Dems look to rebuild 'blue wall' Funding caps, border wall set stage for defense budget battle Trump's claims of defeating ISIS roil Congress MORE (R-Okla.), who is managing the bill in the absence of Armed Services Committee Chairman John McCainJohn Sidney McCainThe Hill's 12:30 Report: Trump steps up attacks on McCain Trump: 'I was never a fan of John McCain and I never will be' Santorum: Trump should 'send emails to a therapist' instead of tweeting MORE (R-Ariz.), said he thought Corker would ultimately be able to get a vote. 

"I think it will. In fact, I told Corker that I would not object to it," Inhofe said, while noting he would vote against the amendment. 

Asked if he thought Corker's bill should get a vote as part of the NDAA, Cornyn said the Senate should have an "open amendment process." 

"It's the source of a lot of frustration here among members when people are denied an opportunity to vote. Back in the good old days ... we used to have [a] much more open amendment process," he said. 

But the process for setting up roll call votes on amendments to the NDAA has ground to a halt in recent years as senators object to a vote on any amendment unless they can also get a vote on their own proposals.

Cornyn noted on Wednesday that there are already objections to amendments as lawmakers jockey for leverage, which could complicate Corker's quest to add his tariff legislation to the defense policy bill.

Business groups, considered a long-standing ally of Republicans, quickly backed Corker's bill.

Neil Bradley, the executive vice president and chief policy officer for the Chamber of Commerce, said on Wednesday that there was concern that Trump's tariff decision would cost American jobs. 

"The constitutional authority of the Congress to 'regulate foreign trade' and its oversight of tariff policy is unambiguous. The modest proposal to clarify congressional prerogatives is welcome and long overdue," Bradley added.

There is no sign that the House is prepared to introduce similar legislation. Asked about the tariff legislation on Wednesday, Speaker Paul RyanPaul Davis RyanPaul Ryan joins board of Fox Corporation Bottom Line Paul Ryan says Trump will win reelection because of 'record of accomplishment' MORE (Wis.) noted that Trump would have to sign the bill.

“You would have to pass a law that he would want to sign into law,” he told reporters. “You can do the math on that.”

Updated at 7:03 p.m.