(CNN) Senate Republicans, for months fearful of -- and outright opposed to -- President Donald Trump's actions on tariffs , now have a bill to tie his hands.

Whether they do anything with it remains an open question.

Sen. Bob Corker, the Tennessee Republican retiring at the end of this term , will introduce a bill Wednesday, and attempt to attach it as an amendment to a must-pass defense policy bill that would require congressional approval for the President to apply tariffs on national security grounds -- a trade tactic the administration has already deployed to justify steel and aluminum tariffs.

The effort faces an uphill climb -- both on the politics and in the strategy, GOP leadership has been wary of the repercussions of moving to directly challenge the President especially in an election year where Republicans are counting on Trump's loyal supporters to keep them in the Senate majority. It's something Corker acknowledged to reporters when he noted "doing anything up here is like pushing a major boulder uphill."

On its face, it's a move that would launch a fight between a Republican Senate and the Republican President and one that would lay bare the broader questions about the role of executive versus legislative powers on trade, spotlighting the simmering intraparty ideological war over how Republicans view trade altogether. It's unclear how much Democratic support exists and there's currently no commitment their House counterparts would follow suit.

And, of course, the President could veto anything sent his way.

"Recognize that any legislative solution has to be signed by the President," said Sen. Cory Gardner of Colorado, echoing a concern GOP leaders have voiced for days.

But several aides say that the idea of doing something has gained traction among the unsettled GOP conference, and may have a shot at a vote in the next week.

Corker's proposal would require the administration to submit to Congress any tariffs proposed on national security grounds, or Section 232, according to a source familiar with the bill. Lawmakers would then have 60 days to approve the proposed actions. The bill would apply to all actions moving forward, as well as those taken at any point within the last two years.

That means it would undercut what has become a primary weapon in the administration's hardline ongoing trade negotiations with countries across the world -- including close US allies in the EU, Canada and Mexico. For all the problems it has created for Republicans on Capitol Hill -- those representing heavy agriculture states have raised the most concern-- Trump has remained steadfast in his approach, one he claims will, in the end, work out.

"The US has made such bad trade deals over so many years that we can only WIN!" Trump tweeted on Monday.

Yet for Republicans, who worked furiously behind the scenes in March to defang the administration's steel and aluminum tariff proposal, it's a fight that has long existed even if the willingness for it to come the forefront was tempered by outside factors.

Several aides told CNN that for months the view was it was more productive to work quietly to register the concerns with the White House, and with the President himself, rather than pose an outright legislative challenge. It's a strategy some Republicans still viewed this week as the best option.

"I don't think there is a legislative response," Texas Sen. John Cornyn, the second-ranking Republican in the chamber, told reporters. "Congress has already given the President pretty unilateral authority on trade matters, so I think we're going to continue have the conversation and use the powers of persuasion."

Asked if those powers of persuasion were effective, Cornyn cracked a grin.

"Sometimes," he said. "Not always, but sometimes."

Aides and lawmakers said the March effort had to some degree succeeded, with the White House crafting exemptions for several close allies -- until the administration announced those exemptions for the EU, Mexico and Canada lapsed this week. Corker wasted little time in jumping in to craft his proposal.

Corker presented the bill behind closed doors to Republican senators Tuesday, to what several said was a positive response, and is targeting the annual must-pass defense policy bill -- which the Senate will take up Wednesday and pass early next week -- as the way to push the proposal into law.

"It was warmly received," Corker said of his presentation. "There will be some who have hesitations over politics."

Senate Finance Committee Chairman Orrin Hatch, who oversees trade policy and is deeply opposed to Trump's trade actions, said Corker "came off well" in his presentation.

Senate Majority Leader Mitch McConnell has been skeptical of pursuing legislation, even as he opposes the administration's actions . But he didn't close the door on an amendment vote in the defense policy bill. "It is open for amendment and we'll see what happens as it moves across the floor," McConnell told reporters.

Corker's effort has been bolstered by another strong-willed supporter: Pennsylvania GOP Sen. Pat Toomey, who sources say has made clear to Republican leadership that trade language needs to be brought up for an amendment vote during the consideration of defense policy bill.

"We have a lot of tactics available to us," Toomey said of his leverage to force a vote on tariffs. "We'll see. I'm hopeful we can do this in a cooperative fashion, but we've got lots of tools available."

It remains an open question where Democrats sit on the bill -- which was still being finalized Tuesday evening. Senate Democratic Leader Chuck Schumer said he still needed to see the proposal. Senate rules require at least a handful of Democratic votes to advance most legislation, given the Republicans' slim 51-49 member hold on the chamber.

Gardner posited that Democrats, many of whom have voiced support for Trump's harder line on trade talks, would balk at the idea of reining him in.

"I think that there's a lot of Democrats who are quietly like 'look, this is great what he's doing,'" Gardner said.

Corker said several Democrats were working with him on the bill and he had bipartisan support. Sen. Heidi Heitkamp, a North Dakota Democrat in a tough re-election fight in 2018, said she was "very interested" in the proposal.

"I'm very concerned about what is happening with trade kind of the whole big picture, and I think at some point here we need to have a discussion about the President's ability to do things that are very disruptive to our economy in a unilateral fashion without congressional approval support," Heitkamp said.