Former Vice President Joseph R. Biden sits at the top of the polls in the 2020 Democratic presidential race, but Iowa Democratic Party officials said he may have already hit the ceiling of his support.

Mr. Biden’s anticipated entry into the race this month has been clouded by complaints by seven women about his overly friendly touching and kissing of them over the years, sparking an intraparty debate over whether the 76-year-old politico is up to speed with the current political culture.

The doubts about Mr. Biden run deeper in the proving ground of Iowa. Democratic officials in counties across the Hawkeye State said his near-universal name recognition accounts for his early lead, but he is so well known that he doesn’t generate the excitement needed to grow his base.

“A lot of people are saying maybe his numbers have peaked,” said Bret Nilles, the Democratic Party chairman in Linn County, the second most populous county in the state and home to Cedar Rapids. “People seem to be leaning toward saying, ‘I want somebody new and somebody energetic.’”

The rift over Mr. Biden appears as a generational split, with opposition coming mostly from younger Democrats who tilt further left or embrace socialist ideas.

But Mr. Nilles, 60, said the thirst for a new leader also comes from Mr. Biden’s generation, who mostly do not object to his hands-on interactions with women in public settings.

“I just got off the phone a couple minutes ago with my mother, and she said, ‘Boy, you know, I really like Joe as a person,’ ” he said, noting that his mother met Mr. Biden during his 2008 presidential run. “And she said, ‘Maybe it is not his time any longer.’ That’s my mother, and she is older than him. She’s 80.”

Mr. Biden twice ran unsuccessfully for president. In 1988, he dropped out before the Iowa caucuses when his run was rocked by a plagiarism scandal in which he cribbed a speech by British Labor leader Neil Kinnock.

Mr. Biden finished fifth in the 2008 Iowa caucuses with less than 1% support and then dropped out of the race.

In Delaware County, Democratic Party Chair Robin Stone said Mr. Biden’s handling of women was the tip of the iceberg.

“He needs to take responsibility and change is behavior, but he is not guilty of sexual assault,” Ms. Stone said. “As far as his presidential aspirations, his policies are also not of the times, and he needs to maintain his elder statesman status and stay out of the race.”

Mr. Biden is expected to enter the race this month and said Friday that he will make an announcement soon.

National polls consistently place Mr. Biden in the lead of the more than a dozen Democrats seeking the presidential nomination.

A Morning Consult poll last week showed him in front with 33% of the vote, followed by far-left icon Sen. Bernard Sanders of Vermont at 25%. The rest of the field was in single digits.

A recent Emerson poll of Iowa voters showed a closer race. Mr. Biden was neck-and-neck with Mr. Sanders, 25% to 24%, respectively.

Democratic strategist Christy Setzer worked on former Sen. Chris Dodd’s 2008 presidential campaign that ended with a sixth-place finish in the first-in-nation Iowa caucuses. She said the early national polls are always a product of name ID and a more accurate picture of the race will emerge in state polls once all the candidates begin interacting directly with voters.

“That said, the knock on older, experienced candidates isn’t limited to Biden and didn’t start this year. Just ask Joe Crowley,” she said.

Mr. Crowley, a longtime Democratic congressman from New York who was thought to be in line for House speaker, unexpectedly lost his job to a primary challenge last year from left-wing upstart Alexandria Ocasio-Cortez.

In his first scrum with reporters since the complaints about being “handsy,” Mr. Biden on Friday said he was sorry that he didn’t understand more how his actions made women uncomfortable, but he refused to apologize.

“I’m not sorry for any of my intentions. I’m not sorry for anything I’ve ever done,” he said.

With nearly 50 years in public life, first as a senator from Delaware and then two terms as President Obama’s sidekick, Mr. Biden said his record supporting women’s rights speaks for itself.

“I’ve never been disrespectful intentionally to a man or a woman. You know, it’s not the reputation I’ve had since I was in high school, for God’s sake,” he said.

Mr. Biden also took on criticism that he had not kept up with the leftward drift of his party.

“The point is the definition of progressive now seems to have changed. It is, ‘Are you a socialist?’ Well, that’s a real progressive,” he said, though he insisted that the Democratic Party had not moved too far left.

“We should have a debate about these things. It’s not a bad thing. But the idea that all the sudden the Democratic Party woke up and, you know, everybody asked, ‘What kind of Democrat [are you]?’ I’m an Obama-Biden Democrat, man. I’m proud of it.”

In Howard County, Iowa, where the Democratic voters tend to be older, party Chair Laura Hubka said caucus-goers are telling her that Mr. Biden is yesterday’s news.

“Unfortunately, more people are telling me that they don’t want Biden to run just because he’s already tried it twice,” Ms. Hubka said.

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