PANAMA CITY BEACH, Fla. — President Trump on Wednesday brought his amped-up roadshow to this spring break playground on the Florida gulf coast, demanding that Democrats stop the “nonsense” of investigating him, mocking Democratic presidential candidates like Joe Biden and Pete Buttigieg, and joking about staying in the White House for another decade.

“After two years, nothing — no collusion,” Mr. Trump told a crowd of several thousand supporters. “Now the Democrats are saying, ‘We want more.’” The congressional investigations of his ties to Russia and the subpoenas of administration officials, he said, were a disgrace.

“It’s time to stop this nonsense,” the president said.

Drawing out investigations after the release of the special counsel’s report, Mr. Trump said, was the only way Democrats could hope to beat him in the 2020 election.

The president seemed to relish the coming campaign, describing the Democratic primary race as a likely “choice between Sleepy Joe and Crazy Bernie,” referring to Mr. Biden, the former vice president, and Senator Bernie Sanders of Vermont. And Mr. Trump took aim at Mr. Buttigieg, a rising star in the early days of the campaign, drawing out the pronunciation of his name (“Boot-edge-edge”) and predicting that Mr. Buttigieg, the 37-year-old mayor of South Bend, Ind., would be a poor match for the president of China, Xi Jinping.