Senator Amy Klobuchar of Minnesota, another moderate, had similar thoughts. “I’m here getting votes,” Ms. Klobuchar said in an interview on Sunday. “It’s not something where I can just — what would be the word — transport in a bunch of ads.” She called on Mr. Bloomberg to “go on the shows that every other candidate goes on, on the Sunday shows and the like.”

She added: “I don’t think I’m going to beat him on the airwaves, but I can beat him on the debate stage.” At a forum on Sunday focused on infrastructure, Ms. Klobuchar, who won the endorsement of The Las Vegas Sun last week, mentioned Mr. Bloomberg early on, referring to President Trump’s comments about his height as she stood to speak. “I am the only candidate that is 5-foot-4,” she joked. “I want that out there now.”

The fixation on Mr. Bloomberg, the free-spending multibillionaire, reflected his rising prominence in the Democratic race, even though he is skipping the first four nominating contests and focusing on the 14 Super Tuesday states that will vote on March 3.

As early voting continued in Nevada on Sunday, some of the criticism seemed to be sticking.

“Bloomberg just has bad connotations that come along with him,” Leah Garwood said as she waited in line with her husband on Sunday in Las Vegas for roughly 45 minutes to vote for a different billionaire, Tom Steyer of California. “It’s just at the back of my mind. It makes me uncomfortable, uneasy.”

Kelly Mays, an English professor who said she favored Ms. Klobuchar and Senator Elizabeth Warren of Massachusetts, called it “a little frightening that you can buy your way in at this late date.” Standing in line to vote on Sunday afternoon, she said she thought Ms. Warren’s chances in Nevada were “probably not great, but I also think people are counting her out way too early.”