WASHINGTON — The casting call came early — the first of many unwelcome interruptions for Kamala Harris since November — consuming the Los Angeles nightclub where she was supposed to be celebrating an uncomplicated Senate victory.

With the polls closed in nearly every other corner of the country, the giant TV above the dance floor left little doubt: Donald J. Trump was almost certainly going to be president. A vacancy — standard-bearer of the Democratic Party, or at least one of them — had come open four to eight years ahead of schedule.

And people had questions.

“Literally everyone was essentially turning to her and asking,” said Juan Rodriguez, Ms. Harris’s campaign manager, recalling the scene backstage on election night. “What does this mean? What do we do?”

The sensation has perhaps grown familiar for Ms. Harris.

Less than eight months later, California’s very junior senator has emerged as the latest iteration of a bipartisan archetype: the Great Freshman Hope, a telegenic object of daydreaming projection — justified or not — for a party adrift and removed from executive power.

“Do we retreat or do we fight?” she thundered in Los Angeles that evening. “I say we fight.”

Like the Senate newcomers Barack Obama or Marco Rubio before her, Ms. Harris — a 52-year-old former prosecutor with a profane streak, a lawyerly aversion to “false choices” and an affection for the rapper Too Short — has insisted that national aspirations are far from her mind.

Like those men, she has not exactly ruled out the possibility, either.

Unlike those men, she is not a man, a fact that has figured prominently in her introduction to mass audiences in a recurring (and highly rated) television series: Senate Intelligence Committee Hearing Into Possible Trump Ties to Russia.

Twice recently, Ms. Harris’s pointed questions and interjections during long-winded witness testimony have prompted uncommon interruptions from Republican colleagues, John McCain of Arizona and Richard M. Burr of North Carolina, the committee chairman, urging her to let the officials answer.

In the outsize fallout, her supporters have questioned whether a white male senator would have been confronted the same way.

“There are times,” said Senator Chuck Schumer of New York, the Democratic leader, “when men don’t like women who are smarter than them.”

Yet this early exposure has obscured a more nuanced Washington debut for Ms. Harris, who seems determined to distinguish her voice from the Democratic pack while offering at least a measure of deference to Senate norms.

In one such nod to rookie humility, she declined to be interviewed for this article, in keeping with an apparent policy against participating in profiles with major publications at this point.

“Oh, God,” she said when approached recently by a New York Times reporter at a congressional softball game. (She smiled through brief pleasantries, clutching a pink pom-pom to cheer her colleagues, before hustling toward the lawmakers’ dugout.)

At the same time, her advisers argue, Mr. Trump’s election has so scrambled the rhythms of the upper chamber that tenure has become a less valuable currency.

“Seniority does not govern all,” said Sean Clegg, a top strategist for Ms. Harris in California. “In effect, all voices are equal.”

This view is not universally shared in the Capitol. Or in her state.

“She just got here,” said Senator Dianne Feinstein of California, when asked about Ms. Harris’s future as a national figure, extolling the virtues of Senate hierarchy and committee-chairing.

The senior senator, now 84, did speak warmly of Ms. Harris, saying she was “on the way to becoming” a good friend.

“What she should do is concentrate on being a good, and possibly a great, United States senator,” Ms. Feinstein said. “The rest will either happen or not happen.”

Ms. Harris’s brushes with national attention predate her Senate election, with a notable cameo from President Obama in 2013. After an event then, he was compelled to apologize after telling a group of Democrats that, in addition to being “brilliant,” “dedicated” and “tough,” Ms. Harris “also happens to be, by far, the best-looking attorney general in the country.”

The daughter of an Indian-born mother and a Jamaican father — raised in a black neighborhood of Berkeley and wheeled to civil rights marches in her stroller — Ms. Harris last lived in Washington as an undergraduate at Howard…