President-elect Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE is using the threat of tariffs to prevent companies from moving jobs out of the United States, an idea that is being met with trepidation by the Republican Party.

Punishing companies for sending jobs overseas would represent a major shift in U.S. trade policy, and one that would have unpredictable effects on the nation’s economic growth.

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Trump has floated a tariff of 35 percent for businesses off-shoring jobs, but it's unclear whether he could move to punish individual companies without the action or blessing of Congress.

Without a detailed proposal, lawmakers are uncertain exactly how the process would work to slap tariffs on companies that cross Trump and opt to ship jobs abroad.

“I don’t know,” House Ways and Means Committee Chairman Kevin Brady Kevin Patrick BradyBusinesses, states pass on Trump payroll tax deferral Trump order on drug prices faces long road to finish line On The Money: US deficit hits trillion amid pandemic | McConnell: Chance for relief deal 'doesn't look that good' | House employees won't have payroll taxes deferred MORE (R-Texas) said in response to a question about how Trump could level tariffs on businesses.

“The president has a great deal of authority on tariffs,” Brady told The Hill. “We would hope he would consult with the constitutional body, the Congress, on the tariff issues.

“But we have time to work through those issues, it’s really early in the transition on trade."

Senate Finance Committee Chairman Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah) said he plans to work with the Trump administration on the best way to achieve the nation’s trade goals.

“We all want effective ways to keep jobs here at home and increase American paychecks,” Hatch said in a statement to The Hill.

“Ultimately, major shifts in policy are decisions that will be made with the consultation of Congress,” he said.

One Senate aide said that any move to slap tariffs on individual companies does not appear to fall into the tariff authorities given to the president.

A House aide said that Congress has broad authority over tariffs but there is uncertainty around the details of Trump’s plan that make it difficult to gauge what might happen.

In all likelihood, Congress would need to sign off on Trump’s plan to levy tariffs on individual companies, trade law experts say.

Under existing laws, Trump could impose tariffs on certain industries but not on individual companies or countries like Mexico and China, as he has suggested.

Any attempt to unilaterally apply a tariff would be illegal and violate U.S. trade deals, the experts argue.

A president has other tools to apply tariffs but they would only come into play under dire circumstances such as in times of war, during a national emergency or if there are questions about national security.

And most of those rules come with limits, according to an aide on Capitol Hill.

In the past week, Trump stiffened his rhetoric on tariffs saying at a Carrier event last week that “companies are not going to leave the U.S. anymore without consequences."

But House Republicans signaled they would not support Trump’s targeting of individual companies as the policy runs counter to their long-held opposition of intervening in the free market.

“I think that's a better way of solving the problem than getting into a trade war with a 35 percent tariff,” House Majority Leader Kevin McCarthy (R-Calif.) told reporters earlier this week over Trump’s threat.

The conservative group Club for Growth said the kind of tariffs that Trump is advocating could tank the economy.

But in general, Republicans have been careful about leveling criticism at Trump and instead have turned the conversation to overhauling the tax code and slashing regulations.

Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.) told a Wisconsin paper this week that lowering business taxes would do more to keep companies in the U.S. than seeking penalties.

Democrats haven't held back and have blasted Trump over the tariff plan.

“Any initiative that we take in terms of trade have a consequence for us,” said House Minority Leader Nancy Pelosi (D-Calif.) on Thursday.

“It doesn't seem well-thought out; it doesn't look like a formula for success; and it certainly will invite reciprocity.”

Many congressional Democrats clashed with President Obama over his trade policies, broadly opposing sweeping pacts like the Trans-Pacific Partnership that promised to slash 18,000 tariffs across the 11 participants.

Rep. Gerry Connolly Gerald (Gerry) Edward ConnollyJudge issues nationwide injunction against Postal Service changes House panel advances bill to ban Postal Service leaders from holding political positions Shakespeare Theatre Company goes virtual for 'Will on the Hill...or Won't They?' MORE (Va.), a pro-trade Democrat, said that Trump likely couldn’t impose hefty tariffs without congressional action and, if he did, the move would prove “catastrophic."

“It’s designed for some PR effect but it’s not a policy,” Connolly told The Hill.

“What are we going to do, is the president going to spend all of his time tracking down any company that has plans to move production facilities overseas?”

Sen. Chris Coons Christopher (Chris) Andrew CoonsMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (D-Del.) said Trump would “have a very hard time doing that and complying with law.”

“It makes great reality TV to pick one company at a time, berate them, go after them and have a partial win,” Coons told The Hill.

“But you can’t do it one company at time, one tariff at time. That’s not going to win in the long-term.”

Naomi Jagoda and Mike Lillis contributed.