Mr. DeSantis, a former congressman who helped found the hard-line conservative House Freedom Caucus, has leaned into the spending fight, and blamed Republicans for overspending during the Trump years.

In a private call this week, which was first reported by Politico, Mr. DeSantis encouraged some of his congressional backers who are also pressing for spending cuts, including Representatives Chip Roy of Texas, Bob Good of Virginia and Thomas Massie of Kentucky. Mr. DeSantis said he supported their efforts, according to two people with knowledge of the call: “Keep fighting,” the governor said.

On Friday, Mr. DeSantis is set to deliver a lunchtime speech to Concerned Women for America while Mr. Trump will address that group in the early evening. Both will speak at the Pray Vote Stand summit in the evening, with Mr. Trump speaking last.

The overlap is also a sign of an intensifying campaign schedule with four months until the Iowa caucuses. Mr. Trump and Mr. DeSantis have made near-simultaneous stops in the same locations throughout the summer, even as Mr. Trump has kept up a relatively light campaign schedule: Both have attended a state party dinner in Iowa, the Iowa State Fair and an Iowa football game.

Mr. Trump skipped the first primary debate last month and is expected to bypass the second debate later this month, meaning that overlapping appearances are opportunities for Mr. DeSantis to sharpen the contrast with the primary front-runner. In an interview with CBS News this week, Mr. DeSantis, 45, spoke about what he argued was voters’ desire for a “generational passing of the torch” in a jab at both President Biden and Mr. Trump, who are 80 and 77.

“The presidency is not a job for someone that’s 80 years old,” Mr. DeSantis said.

Mr. DeSantis and his allies have made disagreements with Mr. Trump over some social policies a focus of the campaign. Last weekend, when Mr. DeSantis and Mr. Trump both attended the Iowa-Iowa State rivalry football game, the pro-DeSantis super PAC, Never Back Down, ran an ad about “transgender insanity,” and used a clip of a decade-old interview that showed Mr. Trump saying he would allow a transgender woman to compete in the Miss Universe competition in 2012.