Senators are moving forward with legislation that would curb President TrumpDonald John TrumpTrump: 'I will not let Iran have nuclear weapons' Rocket attack hits Baghdad's Green Zone amid escalating tensions: reports Buttigieg on Trump tweets: 'I don't care' 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 CorkerCorker: 'I just don't' see path to challenge Trump in 2020 Ex-GOP Sen. Corker: Trump primary would be 'good thing for our country' Pollster says Trump unlikely to face 'significant' primary challenge 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: Stocks sink on Trump tariff threat | GOP caught off guard by new trade turmoil | Federal deficit grew 38 percent this fiscal year | Banks avoid taking position in Trump, Dem subpoena fight Fight over Trump's new NAFTA hits key stretch Former senators launching effort to help Dems win rural votes 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 WarnerOvernight Defense: Congressional leaders receive classified briefing on Iran | Trump on war: 'I hope not' | Key Republican calls threats credible | Warren plan targets corporate influence at Pentagon Key Republican 'convinced' Iran threats are credible Hillicon Valley: Trump takes flak for not joining anti-extremism pact | Phone carriers largely end sharing of location data | Huawei pushes back on ban | Florida lawmakers demand to learn counties hacked by Russians | Feds bust 0M cybercrime group MORE (D-Va.), Lamar AlexanderAndrew (Lamar) Lamar AlexanderIt's time for Republicans to lead (again) on climate WANTED: A Republican with courage Overnight Health Care — Presented by Campaign for Accountability — House passes drug pricing bills amid ObamaCare row | Senate Republicans running away from Alabama abortion law | Ocasio-Cortez confronts CEO over K drug price tag MORE (R-Tenn.), Brian SchatzBrian Emanuel SchatzBullock: Running for Senate 'never really got me excited' Cruz asks Trump FAA pick to 'be pissed off' about Boeing crash deaths San Francisco becomes first city to ban facial recognition technology MORE (D-Hawaii), Ron JohnsonRonald (Ron) Harold JohnsonBarr throws curveball into Senate GOP 'spying' probe Bipartisan group of senators introduce legislation designed to strengthen cybersecurity of voting systems Trump Jr. subpoena spotlights GOP split over Russia probes MORE (R-Wis.), Chris Van HollenChristopher (Chris) Van HollenMnuchin signals administration won't comply with subpoena for Trump tax returns Dem lawmakers urge FCC to scrutinize broadcast workforce diversity Senate fails to override Trump's Yemen veto MORE (D-Md.), Mike LeeMichael (Mike) Shumway LeeBolton emerges as flashpoint in GOP debate on Iran Frustrated GOP senators want answers from Trump on Iran Congress can expand paid leave and help workers save with bipartisan support MORE (R-Utah), Jeff FlakeJeffrey (Jeff) Lane FlakeWANTED: A Republican with courage Protesters who went viral confronting Flake cheered at award event Feinstein to introduce bill raising age to purchase assault weapons after California shooting MORE (R-Ariz.), Ben SasseBenjamin (Ben) Eric SasseSenate Republicans running away from Alabama abortion law Hillicon Valley: Trump signs order to protect US networks from Chinese tech | Huawei downplays order | Trump declines to join effort against online extremism | Facebook restricts livestreaming | FCC proposes new tool against robocalls Huawei officials say they would 'welcome' US ban on tech posing national security risk MORE (R-Neb.) and Johnny IsaksonJohn (Johnny) Hardy IsaksonKlobuchar: Trump plan doesn't deal with 'comprehensive immigration issue' Pence, McConnell eulogize Sen. Richard Lugar On The Money: GOP angst grows over Trump's trade war | Trump promises help for 'Patriot Farmers' | Markets rebound | CBO founding director Alice Rivlin dies | Senate to vote on disaster aid bill next week 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 GrahamTrump, Europe increasingly at odds on Iran Trump: Anonymous news sources are 'bulls---' Trump: 'Good chance' Dems give immigration 'win' after Pelosi called White House plan 'dead on arrival' 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 CornynTrump's immigration push faces Capitol Hill buzzsaw The Hill's Morning Report - Presented by Pass USMCA Coalition - Restrictive state abortion laws ignite fiery 2020 debate Sinema, Gallagher fastest lawmakers in charity race 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 RobertsThe Hill's 12:30 Report: Tough questions await Trump immigration plan Pat Robertson: Alabama 'has gone too far' with 'extreme' abortion law Pat Robertson on if Equality Act passes: The land will 'vomit you out' 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 McConnellBolton emerges as flashpoint in GOP debate on Iran On The Money: Treasury rejects Dem subpoena for Trump tax returns | Companies warn trade war about to hit consumers | Congress, White House to launch budget talks next week | Trump gets deal to lift steel tariffs on Mexico, Canada Schumer calls on McConnell to hold vote on Equality Act 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 InhofeOvernight Defense — Presented by Huntington Ingalls Industries — Trump nominates Shanahan as Pentagon chief | House panel advances bill to block military funds for border wall | Trump defends Bolton despite differences Trump nominates Shanahan as Pentagon chief Iran, Venezuela puts spotlight on Trump adviser John Bolton MORE (R-Okla.), who is managing the bill in the absence of Armed Services Committee Chairman John McCainJohn Sidney McCainPelosi receives John F. Kennedy Profile in Courage Award Romney: Trump 'has distanced himself from some of the best qualities of the human character' MSNBC host: Barr 'the most dangerous person' who works for Trump 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 RyanDebate with Donald Trump? Just say no Ex-Trump adviser says GOP needs a better health-care message for 2020 Liz Cheney faces a big decision on her future 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.