Senators are moving forward with legislation that would curb President TrumpDonald John TrumpTrump claims media 'smeared' students involved in encounter with Native American man Al Sharpton criticizes Trump’s ‘secret’ visit to MLK monument Gillibrand cites spirituality in 2020 fight against Trump’s ‘dark’ values 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 CorkerThe Memo: Romney moves stir worries in Trump World Senate GOP names first female members to Judiciary panel Former US special envoy to anti-ISIS coalition joins Stanford University as lecturer MORE (R-Tenn.) said in a statement announcing the bill.

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In addition to Corker, Sens. Heidi HeitkampMary (Heidi) Kathryn HeitkampOn The Money: Shutdown Day 27 | Trump fires back at Pelosi by canceling her foreign travel | Dems blast 'petty' move | Trump also cancels delegation to Davos | House votes to disapprove of Trump lifting Russia sanction Gary Cohn criticizes the shutdown: 'Completely wrong' EPA's Wheeler faces grilling over rule rollbacks 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 WarnerGeorge Conway on Giuliani walking back Trump Tower Moscow comments: ‘Translation: I made s--- up’ Giuliani says his comments on Trump Tower talks were 'hypothetical' Giuliani: Trump Tower Moscow talks went 'as far as October, November' 2016 MORE (D-Va.), Lamar AlexanderAndrew (Lamar) Lamar AlexanderGrassley to test GOP on lowering drug prices McConnell blocks House bill to reopen government for second time Senators restart shutdown talks — and quickly hit roadblocks MORE (R-Tenn.), Brian SchatzBrian Emanuel SchatzDemocrats signal they'll reject Trump shutdown proposal Trump expected to pitch immigration deal to end funding stalemate Dem senators debate whether to retweet Cardi B video criticizing Trump over shutdown MORE (D-Hawaii), Ron JohnsonRonald (Ron) Harold JohnsonCongress sends bill renewing anti-terrorism program to Trump The Hill's Morning Report — Shutdown fallout — economic distress Hillicon Valley: Republicans demand answers from mobile carriers on data practices | Top carriers to stop selling location data | DOJ probing Huawei | T-Mobile execs stayed at Trump hotel as merger awaited approval MORE (R-Wis.), Chris Van HollenChristopher (Chris) Van HollenDC train system losing 0k per day during government shutdown Senate Dems introduce legislation to back-pay low-wage contractors Government shutdown impasse is a leveraging crisis MORE (D-Md.), Mike LeeMichael (Mike) Shumway LeeHillicon Valley: Trump AG pick signals new scrutiny on tech giants | Wireless providers in new privacy storm | SEC brings charges in agency hack | Facebook to invest 0M in local news AG pick Barr wants closer scrutiny of Silicon Valley 'behemoths' Grassroots political participation is under attack in Utah and GOP is fighting back MORE (R-Utah), Jeff FlakeJeffrey (Jeff) Lane FlakeSchumer recruiting top-notch candidate for McCain Senate seat The Hill's Morning Report — Trump eyes wall money options as shutdown hits 21 days Poll: Sanders most popular senator, Flake least MORE (R-Ariz.), Ben SasseBenjamin (Ben) Eric SasseOcasio-Cortez returns to 'The Late Show' on Monday On The Money: Shutdown Day 26 | Pelosi calls on Trump to delay State of the Union | Cites 'security concerns' | DHS chief says they can handle security | Waters lays out agenda | Senate rejects effort to block Trump on Russia sanctions Senate rejects effort to block Trump on Russia sanctions MORE (R-Neb.) and Johnny IsaksonJohn (Johnny) Hardy IsaksonOn The Money: Shutdown Day 27 | Trump fires back at Pelosi by canceling her foreign travel | Dems blast 'petty' move | Trump also cancels delegation to Davos | House votes to disapprove of Trump lifting Russia sanction Leaders nix recess with no shutdown deal in sight Senators offer measure naming Saudi crown prince 'responsible' for Khashoggi slaying 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 angers Dems by digging into Clinton, Obama controversies Barr’s first task as AG: Look at former FBI leaders’ conduct Debate builds over making Mueller report public 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 CornynGraham angers Dems by digging into Clinton, Obama controversies Trump tells GOP senators he’s sticking to Syria and Afghanistan pullout  Texas governor, top lawmakers tell Trump not to use hurricane relief funds to build border wall 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 RobertsGrassley to test GOP on lowering drug prices Pompeo taking meeting about running for Kansas Senate seat: report Pompeo planning to meet with Pat Roberts amid 2020 Senate speculation 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 McConnellGraham angers Dems by digging into Clinton, Obama controversies Senate GOP eyes 'nuclear option' for Trump nominees next week Taiwan’s President Tsai should be invited to address Congress 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 InhofePressure mounts for Trump to reconsider Syria withdrawal Dems express alarm at Trump missile defense plans Dem senator expresses concern over acting EPA chief's 'speedy promotion' MORE (R-Okla.), who is managing the bill in the absence of Armed Services Committee Chairman John McCainJohn Sidney McCainGrassley to test GOP on lowering drug prices Listen, learn and lead: Congressional newcomers should leave the extremist tactics at home Overnight Defense: Trump unveils new missile defense plan | Dems express alarm | Shutdown hits Day 27 | Trump cancels Pelosi foreign trip | Senators offer bill to prevent NATO withdrawal 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 RyanTrump once asked Paul Ryan why he couldn’t be ‘loyal': book AEI names Robert Doar as new president GOP can't excommunicate King and ignore Trump playing to white supremacy and racism 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.