Mr. Biden’s team has no illusions about Ms. Warren’s skill as a debater and her rise in the polls, advisers and others close to the campaign acknowledge, though they insist that they are not focusing on her alone. Mr. Biden spent the first two debates facing intense criticism from his opponents, a reflection in part of his current standing atop the polls, and his campaign is bracing for more broadsides from all across the stage.

Allies noted that Mr. Biden has survived rough debate performances before, with little lasting impact on his national poll numbers. That, they argue, is evidence of the deep-seated good will that Mr. Biden, President Barack Obama’s vice president, continues to enjoy from the Democratic base.

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They also see several opportunities for him to draw contrasts that could work to his benefit. That list includes emphasizing his foreign policy credentials — as a former vice president and a former chairman of the Senate Foreign Relations Committee — amid several prominent foreign policy-related controversies involving the Trump administration.

His team is convinced that the Democratic electorate is far more moderate than some activists suggest, and welcomes a debate over issues like health care — Mr. Biden supports a public option but opposes eliminating private insurance, something Ms. Warren supports under “Medicare for all” — and which social programs should be offered for free. And allies are eager to deepen an argument Mr. Biden has been previewing: that it is not enough to have ambitious plans if those proposals cannot survive the political realities of Washington.

“Lots of other candidates have great plans, they have good policy papers, many of them have, you know, talked about them on college campuses or in the Senate,” said Senator Chris Coons, Democrat of Delaware. “The difference, I think, is that Joe has decades of actual experience getting things enacted in a bitterly divided and partisan Washington, and I think he can and should point to that.”

Ms. Warren did not face significant scrutiny from other leading contenders in the first two debates. Mr. Biden’s allies are privately hopeful that she will be pressed on the details and practicalities of her proposals by several of the candidates onstage, as her formidable standing in the race now makes her a bigger target for attacks.

Ms. Warren and Mr. Biden have clashed before, exchanging sharp words during a fight over the nation’s bankruptcy laws, which culminated in the passage of a bill in 2005 that Mr. Biden supported and Ms. Warren opposed.