“She’ll be the chief executive of her congressional office, but that is all,” Representative Ileana Ros-Lehtinen, the retiring Republican whose South Florida seat Ms. Shalala is taking. She spent time meeting with Ms. Shalala during the transition to help her adjust. “I want her to understand that she’s used to being the chief, and Congress puts you in your place.”

Ms. Shalala, who weathered a surprisingly competitive primary challenge and general election race, understands the persistent disbelief from both Republicans and Democrats over her decision to run. (“I got pissed off,” she says, watching President Trump doing something — she can’t remember what, but something — on TV.)

And she concedes that her new junior status will be a challenge.

“In my head, I assume it’s a new job, and I’ve got to be careful about not bringing the last job or the last experience to it,” she said, standing in her kitchen with a cup of black coffee.

Ms. Shalala does have some challenges in a Democratic Party that is younger, more diverse and more liberal than Mr. Clinton’s. She must communicate with her district’s significant Hispanic population without fluency in Spanish. As president of the University of Miami, she clashed with custodial workers striking over low pay, though she later earned the support of union workers during the campaign. She enraged Miami environmentalists by selling sensitive and protected land, a decision she insists was within her jurisdiction as university president.

Then there is the affiliation with the Clintons: She served eight years in Mr. Clinton’s cabinet and a year as president of the vilified Clinton Foundation as a personal favor to Hillary Clinton. “Fight Song,” the theme to Mrs. Clinton’s presidential bid, remains Ms. Shalala’s ringtone. (It is her form of resistance, she says.)