Hours before the debate, his campaign also announced that he had decided to support making public colleges and universities tuition-free for many students, adopting a proposal that Mr. Sanders put forward a few years ago. While a nod to the left, Mr. Biden’s move was hardly a display of progressive boldness: Mrs. Clinton offered a similar proposal in 2016 after her primary fight with Mr. Sanders, and the proposal Mr. Biden endorsed is more limited than what Mr. Sanders is advocating in the 2020 campaign.

“For Vice President Biden it’s about a lack of consistency,” Representative Rashida Tlaib, Democrat of Michigan and a Sanders supporter, said in a recent interview. Personal engagement has to be coupled with the embrace of bold policy, she said.

Some activists say the personal outreach could be improved, too.

“We’ve heard from them some but not nearly as much as we’d like to,” said María Urbina, the national political director at Indivisible, a major grass-roots progressive organization. “I think they’ve done a handful of outreach but there are some pretty substantive conversations we’d love to have.”

Still, if he is the nominee, she said, “We will do everything we can to get him elected.”

Mr. Biden is undeniably more moderate than Mr. Sanders, who is a democratic socialist. But Mr. Biden’s allies argue that the former vice president does embrace relatively bold policy — if at a more incremental pace, and on a less sweeping scale, than Mr. Sanders does. Their focus now is on promoting some of those proposals, from gun control to combating climate change, and on learning more about what supporters of other current and former candidates need to hear from Mr. Biden.

“No. 1 is making it clear that we have great respect for Senator Sanders and Senator Warren,” said Mayor Darrell Steinberg of Sacramento, a Biden endorser. “It is important we recognize and understand why young people, many young people, have been driven to that message.”

Internally, the Biden campaign has staff working on outreach to students, young professionals and young elected officials. Many of those officials are then engaging in their own progressive outreach in their cities and states, sounding out local liberal activists, for example, or talking with their fellow elected leaders.

Behind the scenes, a number of Mr. Biden’s congressional allies have also been contacting officials who supported Ms. Warren in particular, both in Congress and around the country.