WASHINGTON — The two rounds of Democratic presidential debates, rather than bringing clarity to the primary or culling the field of 24 candidates, have instead laid bare the fragility of former Vice President Joseph R. Biden Jr. as a front-runner and showcased the divisions over ideology and identity in a party that appears united only in its desire to defeat President Trump.

Having failed so far to dominate the debates, Mr. Biden tried on Thursday to quell liberal resistance to his candidacy by other means: He charged, in Detroit, that certain attacks from the left on his record and his policies amounted to attacks on former President Barack Obama and his legacy.

After nearly 10 hours of nationally televised and often contentious candidate forums, the Democratic hopefuls and their voters are plainly torn over how best to take on Mr. Trump and how aggressive a program they should embrace, particularly on health care and immigration.

And far from coalescing around a possible nominee, Democrats are also sharply divided over what kind of standard-bearer would best bridge the larger generational, gender and racial differences shaping the party in the 2020 race.

“I don’t think anybody is currently perceived as both appealing and low-risk,” said Diane Feldman, a veteran Democratic pollster who said she saw Mr. Biden as having largely given up his advantage on the risk front. “He is still more moderate, he is still of a different generation and those things carry some advantages for him. But he may not still have the ‘low-risk choice’ advantage.”

Mr. Biden demonstrated his vulnerabilities in the two debates, repeatedly offering halting answers, though he performed better in Wednesday’s forum than in the first one in June. But on the stage on Wednesday and at an event on Thursday in Detroit, he also adopted a new strategy: defending Mr. Obama from direct and implicit criticism from some of the other Democratic candidates, particularly Bill de Blasio, the mayor of New York, and Julián Castro, a former housing secretary.

Casting his liberal critics as generally hostile to the administration he served in, Mr. Biden said it was “bizarre” that some candidates were questioning the Obama administration’s record on immigration and other issues, a defensive tactic to remind primary voters of his connection to a respected former president.

The rising tension over Mr. Obama’s legacy, most notably the Affordable Care Act, is a new crack in the party’s orthodoxy, as an ascendant progressive wing that favors transformative change raises questions about the incremental policies of the former president. After a few candidates used the Detroit debate to demand that Mr. Biden account for Mr. Obama’s record on issues such as deportations and free trade, Mr. Biden was joined by some of the former president’s advisers, who chastised the critics for committing political malpractice.

“The more time we spend attacking President Obama and his record and the less time we spend on what Donald Trump is doing to this country only serves to help one person — Donald Trump,” said Stephanie Cutter, a former top Obama campaign aide. “Everybody on that stage needs to keep that in mind.”

David Axelrod, the architect of Mr. Obama’s political ascent, said Mr. Biden would be wise to “lean in” on his ties to the former president and to “confront those who are attacking the Obama policies.” But Mr. Axelrod added that Mr. Biden and the other center-left candidates in the race have so far proved unable to make a compelling, affirmative case for what he called “a reality-based candidacy” that was at once uplifting and pragmatic.

“We ran on ‘yes we can,’ and you’re not going to win on ‘no you can’t,’” he said, recalling the Obama catchphrase.

Ms. Feldman, the pollster, said that a number of Democratic candidates had begun to stand out from the field — including Senators Elizabeth Warren of Massachusetts, Kamala Harris of California and Cory Booker of New Jersey — but that the overall trajectory of the race remained as fluid as ever.

“I think it may be a little less clear today than it was a week ago,” she said.

Among the liberal candidates, Ms. Warren demonstrated her formidable intellect and hard-charging populism at the debates, and Senator Bernie Sanders of Vermont made a full-throated claim to being the architect and chief promoter of ambitious liberal ideas. They delighted many progressives but also left the moderate wing of the party uneasy with their embrace of ideas like eliminating private health insurance, part of an uncompromising agenda the centrists fear will lead to electoral ruin.

Still, the party’s disagreements encompass more than ideology.

There are the divisions of generation and identity, splitting candidates whose gender, race or age would make their presidency historic, like Ms. Harris, who would be the first woman to win. During the debate on Tuesday, it did not go unacknowledged that 40 years of age separated Mr. Sanders from Pete Buttigieg, 37, the mayor of South Bend, Ind., who would become the youngest president in history, while on Wednesday Mr. Biden repeatedly complained that his rivals were pillorying him for “things that occurred a long, long time ago.”

And there are strategic divisions as well, like the debate over whether to prioritize winning back the white voters of the Midwest or energizing African-Americans in cities across the region. In an implicit contrast with Mr. Biden and his focus on blue-collar whites, Mr. Booker described himself on Wednesday as uniquely suited to mobilizing black voters who could be decisive in states like Michigan.

There is something else that alarms establishment Democrats: While Mr. Biden’s grip on the race is clearly tenuous, no obvious, more compelling alternative has emerged from the center-left. And no one is yet in a position to displace Mr. Biden as the front-runner, or as the favorite of moderates and African-Americans.

After surging in the polls and raising about $3 million online in the days after she confronted Mr. Biden in the first debate, Ms. Harris was unable to repeat her performance this week, momentarily confirming the skeptics’ view that she is a lackluster political performer when speaking off the cuff.

Mr. Booker had a stronger turn in Detroit, and was proclaimed the winner in many debate post-mortems, but he is facing significant fund-raising challenges and has already had to consolidate some of his staff.

Numerous other would-be alternatives to the former vice president, like Gov. Steve Bullock of Montana and Mr. Buttigieg, have their admirers but have yet to catch fire with voters in the early nominating states.

And while Ms. Warren and Mr. Sanders electrified the left by stoutly defending their bold proposals on the debate stage, many in the party remain skeptical about their chances to defeat Mr. Trump. More worrisome to their two campaigns is that neither candidate has yet to demonstrate much appeal with African-American primary voters or, in Ms. Warren’s case, working-class Democrats.

“These debates have raised as many questions as they’ve answered so far,” said Ben LaBolt, a former spokesman for Mr. Obama.

Part of the party’s challenge is that Ms. Harris’s viral moment on busing in June, and the higher threshold required to participate in the fall debates, encouraged candidates thirsty for higher poll numbers and more donors to go on the attack and to seek breakout moments. That has led to a stream of acrimonious challenges that sometimes bordered on grandstanding.

Amid the tangle of ideological disputes and personal feuds that dominated the two rounds of debates, it fell at times to lower-profile candidates to exhort Democrats to focus on the bigger picture. Andrew Yang, a former tech executive, issued perhaps the most earnest plea, warning that the race was becoming an affair of “rehearsed attack lines” with candidates “playing roles in this reality TV show.”

“It’s one reason why we elected a reality TV star as our president,” Mr. Yang said, even as he unfurled a rehearsed line of his own.

Not every Democrat is uneasy with a robust argument over the issues.

Mayor Randall Woodfin of Birmingham, Ala., a progressive who attended the debate as a guest of Ms. Harris, said some of the disagreements in the party struck him as valuable, including the drawn-out and occasionally academic discussion of health care. On that subject, he said, there were “actual differences” on policy that merited airing out.

Mr. Woodfin said policy alone would not decide his endorsement in the race. “The ability to win in the general election is equally important,” he said, singling out Mr. Booker for his focus on that task.

“Cory stayed above it, if I’m being honest,” Mr. Woodfin said. “He always brought it back to the general election and beating Trump.”

The race may now head into a long stretch of relative inactivity until the next major opportunity to reorder the contest: another round of televised debates in September, where fewer candidates are likely to muster the polling and financial support required.

But some party officials do not want a repeat of the summer season in the fall.

Voicing the impatience and anxiety of many Democrats, Representative Dan Kildee of Michigan said on Thursday that he planned to “push our candidates to stop’” the intraparty bickering “and talk about the big issues that separate us from Donald Trump.”

“To pretend that we have these big, ideological differences, or to pretend that somehow, some of these candidates aren’t credible messengers on income inequality or injustice — that’s just not true,” Mr. Kildee said. “There’s a real danger when candidates’ individual interests basically trump — I hate to use that term, but trump our mutual interests.”

Asked if he hoped Democrats would settle early on a nominee, Mr. Kildee offered a cold dose of realism: “I don’t think that’s likely to happen.”

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