But Mr. Sanders declined, citing his busy schedule on the trip, said two people familiar with the exchange, who were not authorized to discuss it on the record.

Ari Rabin-Havt, a senior adviser to Mr. Sanders involved in planning the California trip, said he was unaware of multiple requests for Mr. Sanders to help turn out the vote for candidates there.

Perhaps nowhere is Mr. Sanders’s party leadership role murkier, however, than in the way he has approached his endorsements — alone.

“It’s his choice,” said Mr. Rabin-Havt, a senior adviser to Mr. Sanders. “Every decision is his.”

Although some of the roughly 20 candidates he has endorsed do overlap with contenders whom other Democratic and progressive organizations have supported — including Stacey Abrams, an anointed party favorite who is now the party’s nominee for governor in Georgia — he has also confused allies at times by not getting behind winning candidates who support his message. In Nebraska, for example, he did not endorse Kara Eastman, a House candidate and ardent supporter of “Medicare for All,” who swept to victory last month in the Democratic primary over a former congressman.

And where Mr. Sanders has plunged in most directly, voters have not necessarily followed his lead. In Iowa, where he nearly defeated Hillary Clinton in the 2016 caucuses, Mr. Sanders campaigned alongside Pete D’Alessandro, a former aide in his presidential bid, and cut a television ad boosting him in a congressional primary. It had little impact on the race and Mr. D’Alessandro finished a distant third.

Still, even in defeat, Mr. Sanders may be building good will with candidates — and, in many cases, former candidates — who echoed his message, and who say his support brought them new attention from voters and the news media.

“Just a connection with him I think helped my campaign,” said Greg Edwards, who was endorsed by Mr. Sanders but lost his House primary in Pennsylvania.