TOLEDO, Ohio — President Trump’s supporters nodded approvingly last week as Mr. Trump extolled the “big, beautiful monster” of a trade deal that he will sign with China on Wednesday.

The enthusiastic group, gathered at Toledo’s Huntington Center, nodded again as Mr. Trump insisted that America’s farmers, who have been hurt by the trade war with China, were winners and as he asserted, incorrectly, that American importers were not paying for the tariffs.

“And now the deal is done,” Mr. Trump said.

The packed arena roared triumphantly.

On Wednesday, Mr. Trump will sign an initial trade agreement with Beijing that will help cool tensions between the world’s two largest economies but leaves many of the biggest issues unresolved. Key details of the agreement remain murky, the text remains under wraps and more complicated matters, like China’s financial support for companies that compete with American firms, have been pushed until after the 2020 election.

But to Mr. Trump’s most faithful backers, the president took on China and scored a major win.

“Instead of giving all the money to China, now we’re going to get some of it back,” said Kim Lewis, 65, a corn and soybean farmer from Jamestown, Ind., who drove four hours to see Mr. Trump’s speech. “He had the guts to stand up to these other countries.”

The optimism surrounding the outcome of the negotiations reflects the deep trust that Mr. Trump’s supporters have in a president who promised to stop China from “ripping off” the United States and has declared victory in rewriting the terms of trade.

Mr. Trump’s public selling of the deal, along with his rosy views about the American economy, have transcended any downside of his economic policies. Support for Mr. Trump and his trade deal remains strong in places like Ohio, where economic growth and manufacturing employment shows signs of slowing.

National employment data released Friday showed that 12,000 factory jobs were shed in December. Manufacturing employment has been slumping in the industrial Midwest in the last year amid the lingering trade war. Employment in the state’s goods-producing industries decreased by 10,100 from November 2018 to November 2019, according to the Ohio Department of Job and Family Services.

For those devoted enough to Mr. Trump to brave frigid weather and long lines to attend a midweek campaign rally, any responsibility for economic malaise was directed elsewhere.

“Tariffs aren’t the answer, but Trump’s back was put up against the wall,” said Timothy Pedro, the Republican mayor of Waterville, Ohio, who noted that businesses in his town had been holding back investment as a result of trade uncertainty. “He had to do something.”

At the Toledo rally, Mr. Trump steered clear of specifics about the trade agreement, focusing on the promise that it will be enforced with the threat of more tariffs and the commitment he received from China to increase its purchases of American farm products to $50 billion a year — nearly double what it bought at the 2012 peak.

Critics of the deal have said it is unrealistic that China will ramp up its farm purchases so quickly. And they argue that Mr. Trump chose political expediency by settling for an interim agreement that would calm markets amid his re-election campaign but do little to resolve the administration’s biggest concerns about China’s unfair economic practices.

To Mr. Trump’s most ardent backers, however, the piecemeal approach was yet another sign of the president’s deal-making prowess.

“You can’t get everything at one time,” said Jeff Colwell, 54, a car parts manufacturer who lives near Columbus. “Anything we can do to equalize trade with China is a good thing.”

In agreeing to the deal last month, Mr. Trump reduced tariffs he had placed on $360 billion of Chinese goods and opted against taxing another $160 billion of imports. China agreed to enforce stronger protections for American intellectual property, open its markets to American financial institutions and commit to greater transparency surrounding the management of its currency.

The agreement provides Mr. Trump with a policy win to hail, but it also deprives him of a useful foil to rail against. China-bashing is a well-worn tradition for Republicans and Democrats in election years. Former Presidents Bill Clinton and Barack Obama both criticized their predecessors for coddling China despite its human rights abuses and unfair trade practices during their campaigns in 1992 and 2008. As the Republican candidate in 2012, Mitt Romney assailed Mr. Obama for allowing China’s theft of American intellectual property to flourish under his watch.

Mr. Trump has made being tough on China one of his hallmarks and has spent much of his first term assailing it as an enemy and threatening to tax all of its imports. But polling that showed his tariffs were wearing thin on his base and a desire to score a policy victory ahead of the election spurred him to strike an interim deal.

Michael Pillsbury, a China scholar at the Hudson Institute who advises Mr. Trump, said that Mr. Trump’s campaign advisers have realized that the president’s supporters are less concerned about China’s record of human rights abuses or fears that it is an existential threat and more interested in having greater access to its market. He said that Mr. Trump appears to be shifting his tone on China away from the caustic rhetoric used by Stephen K. Bannon, his former chief strategist, in favor of an argument that shows how the president succeeded in “opening up” China.

“The concern of the base about China is not the demonization of China; the concern is the ripped-off jobs and lost trade opportunities, the money part of it,” said Mr. Pillsbury.

Democrats have largely struggled to settle on a forceful critique of Mr. Trump’s China strategy, accusing him of settling for a weak deal and warning that China may ultimately ignore the agreement.

Still, supporters of the president appear ready to blame China, rather than Mr. Trump, if the deal does not hold.

Randy Rothenbuhler, who owns a corn and soybean farm 45 minutes south of Toledo, said that his soybeans had been piling up in bins for the last year because of Chinese retaliation. He is hopeful that the new agreement will mean the reopening of China’s market, but he will remain skeptical until he sees it happen.

“That’s the billion-dollar question, will China live up to its promise?” Mr. Rothenbuhler, 42, said. “We’ll have to wait and see.”

Although Mr. Trump might have to shift away from lashing out at China in the wake of the agreement, he appears likely to make the case that he alone could have struck such a deal and that no one else can hold China to its word.

“They’re going to do what he wants them to do,” said Michelle Sellati, a forklift driver from Lima, Ohio. “If China just works with Trump, they’ll benefit, too.”