Vivek Ramaswamy blasted through eastern Iowa on Tuesday with the breakneck speed that has become characteristic of his improbable presidential campaign.

At most of his six scheduled restaurants and bars visits, he paused only briefly to remind voters of his presence before lingering longer at his final stop. His candid, bombastic style garnered praise, and his humorous comments, such as promising to finish the task of draining the bureaucratic swamp in Washington by “bringing the pesticide,” resonated with the attendees.

However, the day served as a stark reminder of how deeply entrenched Mr. Ramaswamy remains in his own kind of swamp, lagging far behind his Republican rivals and trailing in fourth place in most state polls. In Dubuque, minutes before his arrival at a cozy cocktail bar for a speech, only about five of the 50 attendees raised their hands when asked how many planned to caucus for him.

Some voters at his six Iowa events wondered whether he was merely enhancing his credentials for a 2028 presidential run or a position in Mr. Trump’s cabinet if the former president were to be reelected.

“I think he’s got a really good chance of that,” said Matt Casey, 49, regarding a potential role for Mr. Ramaswamy in a Trump administration. “He could probably be the vice president real easy.”

Mr. Ramaswamy, who largely financed his presidential bid from earnings in his biotechnology business, can afford to remain in the race for as long as he desires. He has maintained that he will defy expectations and achieve an underdog victory on the January 15 caucus night, arguing that many of his supporters are young people and other first-time caucusgoers not reflected in the polls.

“I think we’re going to deliver a major surprise,” Mr. Ramaswamy told reporters on Tuesday.

His strategy of aligning closely with Mr. Trump’s policies and praising the former president has earned him accolades and respect from Iowa Republicans. But with less than two weeks remaining until the caucuses, voters’ support for Mr. Trump remains unwavering, leaving Mr. Ramaswamy as the second-favorite for many.

“I’d like to see a Ramaswamy presidency, but I think he’s got a steep hill to climb,” said Jeremy Nelson, 46.

Mr. Ramaswamy portrayed himself as a more refined version of Mr. Trump, quoting former President John Quincy Adams and expressing his commitment to political ideals. He mentioned a wide variety of issues and derided Mr. Trump’s reliance on political advisers.

Sandy Kapparos, 75, said she was “very impressed” with Mr. Ramaswamy’s wide grasp of various issues.

However, Mr. Ramaswamy’s chances of winning the nomination have diminished, prompting him to deploy desperate measures. He acquired novelties such as an endorsement from Steve King and delved into far-right rhetoric. He also rented an apartment in Des Moines, campaigned through Thanksgiving, and completed the so-called Full Grassley tour through each of Iowa’s 99 counties.

Mr. Ramaswamy is far from the first long-shot presidential candidate to linger in a primary longer than expected and, despite the odds, staying in a race can increase name recognition and other benefits.