“When she came into this race she had near-universal favorable ratings with Democrats,” said Mo Elleithee, executive director of the Georgetown Institute of Politics and Public Service. “She needs to come in and remind people what they like about her, what they still like about her, and make an assertive, compelling case for herself that is about more than just inevitability.”

Mr. O’Malley is hoping the chance to sell his executive experience and liberal policy prescriptions, including breaking up commercial and investment banks, to a prime-time audience will give his stalled candidacy some fresh momentum.

For Mr. Sanders, the debate is an opportunity to widen his appeal and persuade skeptical Democrats that he would be a viable nominee. Aides say he needs to flesh out his big policies but also talk about incremental achievements he won during more than two decades in Congress.

“She needs to be aggressive in providing a contrast with Sen. Sanders without going over the top,” said Jim Manley, a Democratic strategist. “A lot of people will be tuning in to the campaign for the first time ?and she is going to have to show them that she is ready to fight for their vote.”