Over the past four months, Gavin Newsom, the Democratic governor of California, has traveled to six Republican-led states. He has goaded Gov. Ron DeSantis, the Republican presidential candidate from Florida, to debate on Fox News. He has assembled a small staff of political advisers and created a political action committee to distribute $10 million to Democratic causes and candidates.

And this week, he raised $40,000 for a long-shot candidate for the United States Senate in Tennessee, one of the red states he has criticized his own party for neglecting.

By all appearances, Mr. Newsom is a man with an eye on the White House, building a national network of supporters and accumulating the kind of good will among donors, party operatives and voters that could prove critical should he decide to move beyond Sacramento. Mr. Newsom said in an interview that he was not running for president, and that the time has come for Democrats to rally around President Biden.

“The train has left the station,” Mr. Newsom said. “We’re all in. Stop talking. He’s not going anywhere. It’s time for all of us to get on the train and buck up.”

But it may be difficult for Mr. Newsom to quiet speculation about his own future. He has spent months positioning himself as one of his party’s leading voices during a time of deep Democratic worry and lingering unease about the political strengths of Mr. Biden, who is 80, and his vice president, Kamala Harris.

A CNN poll released on Thursday found that 73 percent of all respondents were “seriously concerned” that the president’s age might affect his mental and physical competence. Some 67 percent of Democrats said the party should nominate someone else.

Mr. Newsom has, by his account, sought to reassure the White House in both public and private that he is no threat to Mr. Biden’s re-election campaign. And in turn, Mr. Biden’s team has appeared to pull him closer. The governor will be a top Democratic surrogate defending Mr. Biden when Republican candidates debate at the Ronald Reagan Presidential Library later this month.

This dance — of raising one’s profile without undercutting the president — is the challenge for a class of Democrats-in-waiting, which also includes Gov. J.B. Pritzker of Illinois and Gov. Gretchen Whitmer of Michigan. But Mr. Newsom, a 55-year-old telegenic, popular-in-his-own-state leader, has made himself the most visible in this group, and he may serve as a reminder of Mr. Biden’s shortcoming as he seeks re-election.