Sen. Ben Sasse, R-Neb., a frequent Trump critic, argued that a 35 per cent tariff would be passed along to American consumers in the form of higher prices.
"Pres-Elect Trump means well. But won't his 35% tariff idea raise prices on American families? How would it not be a new 35% tax on families?" Sasse wrote on Twitter.
A conservative advocacy group, the Club for Growth, said that it favors Trump's proposals on tax and regulatory changes but warned of the consequences of cutting off trade.
"We think it's bad economic policy. It'll cost more American jobs than it saves" said former Indiana congressman David McIntosh, the head of the Club for Growth. "Therefore it needs to be stopped."
Trump's threat Sunday also put American companies in an extraordinarily difficult position. Offshoring has been a key element of corporate America's strategy in recent decades, and major lobbying groups have been defenders of trade agreements. But groups stood nearly silent on Sunday, potentially worried about drawing the wrath of the president-elect.
The U.S. Chamber of Commerce, the nation's largest business lobby, declined to directly respond to Trump's comments but signaled that it has not budged in its opposition to tariffs.
"We are not going to comment on Trump's comments directly, but in general, the Chamber has always called for pro-growth policies that help American companies succeed globally and welcome foreign investment within our borders," said Blair Latoff Holmes, a spokeswoman for the group.
She pointed to a recent Fox Business Network interview in which the Chamber's chief economist said that tariffs are "self-destructive."
Last week, Trump made clear he would intervene in specific situations in which companies are considering moving work overseas. Last week he traveled to an Indiana factory owned by furnace and air-conditioner manufacturer Carrier to champion a deal to keep about 800 jobs in the United States. To much criticism, Carrier had planned to move them to Mexico.
On Sunday, Vice President-elect Mike Pence said that Trump would continue the extraordinary interventions, working on deals with such companies "on a day-by-day basis."
Although Trump would be able to follow through on some of his threats without congressional approval - for example, declaring China a currency manipulator and launching a renegotiation of the North American Free Trade Agreement - it's not clear whether he could penalize companies broadly for moving jobs overseas without congressional authorization.
Gary Clyde Hufbauer, a senior fellow at the Peterson Institute for International Economics, a think tank that regularly supports proposed trade deals, predicted that Trump would face legal obstacles if he tries to impose tariffs on individual companies unilaterally.
"This would be, in my way of thinking, a real intrusion of congressional powers over foreign commerce," Hufbauer said. "We've never had this kind of policy before, so he's on novel ground."
During the past few decades, the prevailing view in the Republican Party has been to favor free-trade deals and oppose tariffs. House Speaker Paul Ryan, Wis., for instance, has argued against the government "picking winners and losers."
Spokesmen for Ryan and Senate Majority Leader Mitch McConnell, R-Ky., offered no comment on Sunday.
In his interview with ABC's "This Week With George Stephanopoulos," Pence rejected the idea that Trump will be picking winners and losers.
"What the president-elect did with Carrier was simply reach out, one American to another, and just ask them to reconsider," Pence said. "He told them, we're going to do exactly what we said we would do in this campaign, we're going to make the American economy more competitive, we're going to get tougher and smarter on trade deals."
Tom Davis, a former Virginia Republican congressman, said that Trump is realigning cultural and economic issues and the way voters have historically associated them with the two parties. But he predicted Republicans leaders wouldn't instantly fall in line behind him.
"I don't think it happens overnight. It's evolutionary, it's not revolutionary. You'll see more and more Republicans move to align on the trade issue with Trump, especially in the rural areas," said Davis, who described himself as an "avid free trader."
Trump celebrated the Carrier deal - in which Indiana promised to provide Carrier about $7 million in incentives, while the company would invest $16m in the factory over the next two years - with a tour of the factory last week, followed by a rally in Cincinnati to kick off his "thank you" tour.
On the stump, Trump espoused an aggressively protectionist stance toward international trade, and his skepticism of the benefits of globalization resonated with many middle-class voters who bore the brunt of its downside. Even some leading liberal Democrats acknowledged that his elements of economic message broke through with working-class voters and opened up the possibility of working with him on shared areas of interest.
But since his election, his advisers have softened some of his most heated rhetoric. Trump's picks for treasury secretary, Steven Mnuchin, and commerce secretary, Wilbur Ross, said that they would pursue bilateral trade agreements with other countries but remained wary of sweeping regional deals. Ross also said that blanket double-digit tariffs on goods from Mexico and China - which many economists warned could spark a damaging trade war - would be used only as a last resort.
Still, Trump's social-media message on Sunday served as a signal that the Trump who appeared on the campaign trail at raucous rallies and boasted about his ability to shake up Washington isn't going away.
"Please be forewarned prior to making a very . . . expensive mistake!" Trump wrote on Twitter. He continued, in all capital letters, "THE UNITED STATES IS OPEN FOR BUSINESS!"
