When President Biden said he would drop out of the presidential race just over a week ago, throwing his support behind Vice President Kamala Harris, a jolt of energy instantly excited a beleaguered Democratic base.

The party rallied around Ms. Harris, as upbeat memes and positive statistics for Democrats over the past week abounded: $200 million in contributions, a litany of tantalizing vice-presidential options and a rash of improved polling.

Ms. Harris now faces harder tasks in the coming weeks: maintaining that enthusiasm as the initial excitement fades, as former President Donald J. Trump and his campaign sharpen their attacks against her.

This week alone has important mile markers. Democratic delegates could begin voting to virtually nominate Ms. Harris as early as Thursday, the date the Democratic National Committee said they were expected to do so if only one candidate emerged.

And the running mate speculation will be rampant this week, as Ms. Harris narrows her choice, with Aug. 7 as a deadline she has set. She has empowered Eric H. Holder Jr., the former attorney general, and his law firm, Covington & Burling, to vet the prospective candidates.

“I would call it a honeymoon phase,” said Steve Sisolak, the former Democratic governor of Nevada, a key swing state. “We’ve got to keep the energy going. You got it started — now you’ve got to keep it going. It’s going to be a challenge for everybody.”