Outside groups, however, are pushing Republicans to support Corker's legislation.
Sen. Lindsey Graham, R-S.C., came away from a meeting with Trump opposed to Corker's legislation.
A group of senators are crafting a plan that would claw back some of President Donald Trump's authority to enact sweeping tariffs and other trade policies that many Republicans and other free-trade supporters believe would result in lasting damage to the United States economy.
"Mitch is using any excuse he can to hold those of us who want to be home campaigning here in Washington because we have to vote", Nelson told reporters Tuesday.
But he says he'll pitch the idea more broadly when Republican senators convene Tuesday for their weekly lunch.
"Now is not the time to undercut President Trump's ability to negotiate better trade deals".
"I tried to explain to the Lt. Governor that it's out of order, otherwise any bill that was plopped on the desk could start a debate immediately".
Five Republicans and four Democrats signed on as co-sponsors to Corker's bill. "We'll see. I'm hopeful we can do this in a cooperative fashion, but we've got lots of tools available".
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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. Mexico, for instance, is imposing a 20 percent tariff on USA agricultural products including apples and 25 percent duties on Tennessee whiskey in response to Trump's trade policies.
Several lawmakers have said justifying tariffs on national security grounds was hurting US credibility and inviting retaliation that would hurt an otherwise solid economy.
This has anxious some Republican lawmakers who strongly back principles of free trade, warning that Trump could trigger a trade war that would destabilize the economy and ultimately hurt American workers.
They're trying to produce narrowly drafted legislation that would allow Congress to weigh in on the administration's claim that the tariffs are needed for national security. The legislation would qualify for expedited consideration for a 60-day period.
Corker isn't alone on his side of the aisle. Sen. Pat Toomey of Pennsylvania, Lamar Alexander of Tennessee, Ron Johnson of Wisconsin, Mike Lee of Utah, Jeff Flake of Arizona, Ben Sasse of Nebraska and Johnny Isakson of Georgia.
"I commend Sen. McConnell for extending the summer legislative session in the face of unprecedented Democratic obstruction". Heidi Heitkamp of North Dakota, whose significant number of agricultural constituents could bear the brunt of retaliatory policies from allies and trading partners unhappy with the new tariffs.
The proposal will be offered as an amendment to the annual National Defense Authorization Act, which is must-pass legislation and makes the prospect of a presidential veto that much more hard on the White House's end.
"I want the Senate to take up those 500 bills that are sitting there that passed in the House and get those through", said House Majority Leader Kevin McCarthy, R-Calif.
It's not as though the current Congress accomplished so much that it needs the break.