HOUSTON — Democratic presidential front-runner Joseph R. Biden has proved remarkably resilient to attacks, gaffes and health scares. Now his unshakable lead in the polls has his political allies fighting off the perception that he is becoming the inevitable nominee.

The aura of inevitability can be a campaign killer, sapping supporters’ enthusiasm and depressing turnout for the only polls that matter: the caucuses and primaries. Just ask Hillary Clinton how inevitability turns into startling defeat on Election Day.

“That is a dangerous mindset to have. You have to always think that your opponents are right on your tail and keep fighting as hard as you can,” said Jon Cooper, a major Democratic fundraising bundler who is backing Mr. Biden.

Mr. Biden will be taking that mindset to the stage Thursday when he joins nine of his rivals for the Democratic presidential nomination in Houston.

Mr. Cooper said he is confident Mr. Biden will secure the nomination because the former vice president is widely viewed as the best candidate to beat President Trump. However, he expected the race to tighten and eventually become a three-way contest among Mr. Biden and two far-left contenders, Sens. Elizabeth Warren of Massachusetts and Bernard Sanders of Vermont.

“Nothing is inevitable in politics. Things can change dramatically from one week to the next. But I think he will be the nominee,” Mr. Cooper said. “His lead will be maintained and solidified, and at the end of the day, when he faces the final challengers in the primary, he will be very well positioned.”

Ms. Warren and Mr. Sanders will be flanking Mr. Biden on the debate stage Thursday.

Sen. Kamala D. Harris of California; Mayor Pete Buttigieg of South Bend, Indiana; Sen. Cory A. Booker of New Jersey; Sen. Amy Klobuchar of Minnesota; entrepreneur Andrew Yang; former Rep. Beto O’Rourke of Texas; and former Housing and Urban Development Secretary Julian Castro also will have their chance to dent Mr. Biden.

Mr. Biden, however, has shown an uncanny ability to bounce back whenever his rivals appear to have him on the ropes.

In the June debate in Miami, Mr. Biden fumbled for an answer when confronted by Ms. Harris for his opposition in the 1970s to federally mandated busing to integrate public schools.

But the attack by Ms. Harris, a woman of color, failed to dislodge black voters, who overwhelmingly prefer Mr. Biden. Instead, black voters in places such as early-voting South Carolina rallied behind Mr. Biden.

South Carolina state Rep. Beth Bernstein, who has endorsed Mr. Biden, said his staying power comes from the fact that people know him after eight years as President Obama’s right-hand man and more than 30 years in the Senate.

“No matter what people are going to sling at him, people really see the true Joe,” she said.

The challenge for Team Biden is managing expectations. At this point, a dip in the polls for Mr. Biden would be regarded as a sea change in the Democratic race.

Others have caved under similar circumstances. Former Texas Gov. Rick Perry blasted into the 2012 Republican presidential race with sky-high expectations only to crash after a cringeworthy debate performance.

The Biden campaign is walking a fine line between touting his front-runner status and playing down the impression that he is running away with the nomination.

When a recent national poll by Monmouth University showed Ms. Warren and Mr. Sanders inch ahead of Mr. Biden by a single percentage point, the Biden campaign reached out to reporters to call the survey “an outlier” and impugn its methodology.

“Poll after poll also confirms that, because of the high stakes of this election, Democratic primary voters are the most energized about a nominee who can take on and defeat Donald Trump and the atrocious values he represents, and win the battle we’re in for the soul of this nation,” a Biden campaign official said. “Joe Biden is by all accounts the candidate best positioned to make that happen.”

Indeed, most polls showed Mr. Biden sustaining a big lead regardless of his stumbles and traumas on the trail.

Concerns about the health of Mr. Biden, 76, resurfaced last week when blood pooled in his eye during a CNN town hall forum on climate change.

The red eye was assumed to be a subconjunctival hemorrhage, which occurs when a tiny blood vessel breaks just underneath the clear surface of the eye. It is usually harmless, but it rekindled memories of Mr. Biden’s near-fatal aneurysms in the 1980s.

Mr. Biden later said he poked himself in the eye while removing a contact lens. “It was my contact lens,” he told The Laconia (Iowa) Daily Sun. “I think I — you know when you’re taking it out — I think bruised my eye.”

A poll released Tuesday showed the eye incident didn’t ding Mr. Biden as he once again scored a double-digit lead. He was the top choice of 33% of potential Democratic primary voters, followed by Mr. Sanders at 21% and Ms. Warren at 16%, the Morning Consult poll found.

The results were largely in line with the weekly tracking poll since July.

Ms. Harris was next at 7%, followed by Mr. Buttigieg at 5%. Mr. O’Rourke, Mr. Booker and Mr. Yang were tied at 3% each.

“One of the challenges about front-runner status is that there are additional pressures that other campaigns don’t face,” said Democratic strategist Zach Friend, noting the extra scrutiny of debate performances, the dissection of every poll and the expectations of a top finish in the leadoff Iowa caucuses.

“For Vice President Biden, his polling has been resilient, but as the race settles into a top three or five candidates, it will be interesting to see if the polling continues its resiliency as candidates drop out and the race becomes more focused,” Mr. Friend said.

“The one unifying factor across the Democratic Party is the bumper sticker that says ‘The Democrat 2020.’ Meaning Democrats want someone that can win in November of 2020, and as long as Vice President Biden is seen as a leader in that narrative, then it seems likely that he will be one of the leaders in delegates heading into the convention next year,” he concluded.

⦁ Seth McLaughlin reported from Washington.

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