But Mr. Becerra also said he saw his future in the House, where he hoped to help lead a major overhaul of immigration laws that Mrs. Clinton has promised to pursue if she wins the White House.

Unlike Representative Chris Van Hollen of Maryland, another rising star in the party who decided to run for the Senate this year rather than wait for other leadership positions to open up in the House, Mr. Becerra declined to seek the seat being vacated by Senator Barbara Boxer of California, who is retiring.

While a Senate race would have been an expensive and risky bet — a run for mayor of Los Angeles in 2001 was a total flop, getting him just 6 percent of the primary vote — winning re-election to the House is a near certainty in his heavily immigrant downtown district, which includes parts of Chinatown, Koreatown and Boyle Heights, a largely Hispanic area. In 2014, Mr. Becerra won 72.5 percent of the vote, a low total for him, only because under a new primary system, he faced a fellow Democrat in the general election. In 2012, the last time he ran against a Republican, Mr. Becerra won 85.6 percent of the vote.

By staying in the House, Mr. Becerra seems to be betting that his arduous campaigning on behalf of Mrs. Clinton — he has held events for her in 10 states and made countless television appearances — and his work to support fellow House Democrats will secure him a continued role in leadership, even if the path is so far uncertain.

In the meantime, he seems to relish his role on the presidential campaign trail, and the speculation that comes with it. For those who play the insider game, Mr. Becerra was part of a three-person presidential delegation to the Vatican for the canonization Mass for Popes John XXIII and John Paul II in 2014. Joining him were John Podesta, the Clinton campaign chairman, who is expected to lead the vice-presidential selection process, and Katie Beirne Fallon, President Obama’s former legislative affairs director, whose husband, Brian Fallon, is a spokesman for the Clinton campaign.

Despite such connections, conventional wisdom would suggest that Mrs. Clinton, in a race against Mr. Trump, would need to broaden her appeal among white men. Still, Mr. Trump’s unorthodox candidacy may make traditional calculations obsolete. Mr. Torres said Mr. Becerra would have a lot to offer the Democratic ticket, as a son of Mexican-American immigrants who went on to get economics and law degrees at Stanford, and whose reputation is unblemished. Mr. Becerra and his wife, Carolina Reyes, an obstetrician who specializes in high-risk pregnancies, have three daughters.