“It’s probably the No. 1 thing that influences my vote,” he said.

Mr. Knight, who runs a start-up in Dallas that makes software for the construction industry, said he was not sure how much credit Mr. Trump deserved for the strong economy. But he said his customers have benefited from the administration’s efforts to ease regulation, and he said he supported the president’s approach on trade, even though it had driven up some costs.

“I think we have the resources to outlast China, hands down,” he said. “I think it’s a smart move.”

Republicans are counting on voters like Mr. Knight to carry Mr. Trump to victory in November. The president routinely promotes strong economic data and the rising stock market in speeches and at rallies.

“Are you better off now than you were three years ago?” he asked on Twitter on Tuesday. “Almost everyone says YES!”

That argument ran into trouble over the summer when turmoil in financial markets and escalating trade tensions with China and other countries led to a surge in news coverage warning of a possible recession. Measures of consumer confidence fell in September and were slow to rebound.

Economic growth cooled last year, according to data released by the Commerce Department on Thursday, and forecasters expect momentum to slow further in 2020. Still, recession fears have ebbed in recent months, as the job market has remained strong and the Federal Reserve has taken steps to prevent damage from the trade war from spreading to the broader economy. Now confidence appears to be rebounding as well.

“There was this dark cloud hanging over us, but a lot of that has lifted,” said Joseph Song, an economist at Bank of America Merrill Lynch. He noted that wage growth had been picking up among lower-income workers, which could further bolster their economic outlook.

Another factor could also be driving confidence: the stock market.

Mr. Trump frequently cites the rising market as evidence that his policies are working. Experts generally reject that argument: Most Americans own few stocks, and the relationship between stock prices and economic growth is erratic at best. But research has found that the performance of major stock indexes can have a powerful influence on consumers’ outlook.