Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) signaled on Wednesday that he will not support legislation reining in President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE's tariff authority and that the president will not sign such a bill.

"Yeah, I don't think we need to be trying to rein in the president through legislation. No. 1, it would be an exercise in futility because he wouldn't sign it," McConnell told SiriusXM when asked if he opposed the bill.

The legislation is backed by roughly a dozen senators so far, with several others indicating they are studying the bill, which was rolled out on Wednesday afternoon.

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Trump sparked backlash from GOP senators after the administration went forward with slapping tariffs on steel and aluminum imports from the European Union, Canada and Mexico. The administration is also weighing a tariff on imported autos.

The White House is stepping up its efforts to squash any momentum, as supporters look to try to get a vote as soon as this week on attaching the tariff legislation to an annual defense policy bill.

McConnell told SiriusXM that he was "concerned" about the Trump administration's tariff decisions, adding that he hopes "this doesn't develop into a full-scale trade war."

McConnell's opposition to the bill comes after he told reporters on Tuesday that he would not bring Corker's bill up on a stand-alone measure and said late last week that there was "not much" Congress could do legislatively.

"I think the best tool for those of us who are concerned about this devolving into a full-scale trade war is to continue to try to convince the president that we need to not let this go on to long or go too far," McConnell added on Wednesday.

Opposition to the bill from McConnell and the White House could prove critical to squelching support for it in the Senate, where the GOP leader is well respected and many Republican senators are wary of crossing the White House months before a midterm election.