Ms. Gillibrand was the first in her caucus to say Senator Al Franken of Minnesota should resign. She was the first prominent Democrat to say President Bill Clinton should have left office for his own sexual misconduct in the 1990s. She called for Mr. Trump to step down, citing his “numerous” and “credible” accusers. Then came Mr. Trump’s Twitter counterpunch, which was widely viewed as innuendo-laden and which Ms. Gillibrand denounced as a “sexist smear.”

Yet Ms. Gillibrand’s strengthening hand in national Democratic politics owes to more than mere circumstance. Circumstance does not transform an upstate congresswoman, who once boasted of keeping guns under her bed and pushed English as the official language of the United States, into an avatar of progressivism in 2017.

Ever since her long-shot entrance into a 2006 House race against an entrenched Republican in a conservative district, Ms. Gillibrand has been underestimated. Colleagues in the House once derided her as “Tracy Flick,” the hyper-ambitious blonde played by Reese Witherspoon in the movie “Election.” And when David A. Paterson, New York’s governor at the time, made her the shock pick to fill Hillary Clinton’s Senate seat in 2009, she was immediately seen as vulnerable, especially from the left.

“She had very middle-of-the-road points of view,” Mr. Paterson said. “It just kind of appeared that she sort of flipped. I think in retrospect, it would have been better to evolve.”

That knock has not stuck, and she appears to be looking at the next rung of the political ladder. While Ms. Gillibrand and her political team play down all talk of 2020, saying she is focused on her own 2018 re-election and those of her fellow Senate Democrats, she has for months been doing the type of spadework endemic to past presidential candidates: expanding her fund-raising network, courting key constituencies like black voters and polishing her image nationally.