Among Ms. Warren’s goals in the near term are to consolidate her backing from liberals and expand her appeal to lower-income voters and minorities. Attacking Mr. Biden might not serve either goal. In the debate, Ms. Warren spent far more time highlighting her upbringing in a working-class Oklahoma family than engaging on any level with Mr. Biden. She must also still navigate the enduring presence of Mr. Sanders on the left.

And Mr. Biden may have more immediate challenges. On Thursday night, he repeatedly expressed himself imprecisely — saying at one point that no nonviolent criminals should be in jail, when he meant to refer only to nonviolent drug offenders. He also referred to himself as the vice president of the United States, without appending the modifier “former.”…

In Mr. Biden’s camp, there is a persistent sense that his rivals and the news media are underestimating him and giving him too little credit for the blocs of support he has already claimed. Whatever the flaws in Mr. Biden’s performance in Houston, there was no exchange in which an opponent obviously routed him, as Senator Kamala Harris of California did in the first debate and Mr. Booker did in the second.