Biden struggles to manage the Democratic Party’s competing interests.

President-elect Joseph R. Biden Jr. is confronting outbreaks of factionalism and fierce impatience within his own party, as the groups that make up the Democratic coalition see President Trump crumbling as an adversary and turn instead toward the battle to define the personnel and policies of a new administration.

The competition for senior offices has strained valuable political alliances, vexing some of Mr. Biden’s key supporters from the Democratic primary contest, as well as numerous minority and female lawmakers on Capitol Hill.

Mr. Biden has so far sought not to muffle Democratic dissension or impose a tightly focused message on the party, but rather to roll out a team focused on addressing the coronavirus crisis while placating various interest groups.

It remains to be seen whether Mr. Biden will attempt a more assertive approach once he takes office. Advocacy groups from across the Democratic coalition have been mobilizing to demand swift executive action on matters from student debt and police overhauls to union rights and climate change.

Representative Alexandria Ocasio-Cortez of New York, a prominent progressive, said she hoped Mr. Biden would soon lay out the overarching themes of his administration, going beyond the week-by-week staff announcements.

Some lawmakers are also complaining that they have not been adequately consulted by Mr. Biden and his team on appointments, especially the selection of Lloyd J. Austin III, a retired general, for defense secretary, given that his recent military service will require Congress to grant him a special waiver.

In addition, there is mounting angst among some of Mr. Biden’s allies that people who fought hard for him during the campaign have found themselves waiting in line for jobs while Obama-era holdovers were quickly slotted into senior roles.

So far, the president-elect and his advisers have tried to manage conflict from something of a careful distance, holding listening sessions with various Democratic constituencies and then holding deliberations within Mr. Biden’s tight inner circle, eventually unveiling personnel decisions in batches aimed at pleasing several groups at once.

Mr. Biden’s choices stem from his determination to fulfill his promise of appointing a cabinet that reflects the diversity of the country. And his aides have privately been working to salve wounds by telling people there will be turnover in the top jobs soon enough.

In the meantime, Democrats say, Mr. Biden may continue to receive help from a familiar source in his bid for party unity.

Representative Ro Khanna, a California progressive, said there was still enough “fear of Trump” in the Democratic coalition to offer Mr. Biden an ongoing “grace period.”

“Trump continuing to float that he’s a candidate in the future may be a blessing for Joe Biden,” Mr. Khanna said. “It may be what Joe Biden needs to keep the Democratic coalition together.”