Ms. Collins, 67, has a strong relationship with Mr. Biden, who has called her “a woman of incredible character, integrity, and grace.” And now, she has the battle scars and enhanced credibility that comes with having accomplished a feat many Republicans readily concede they never could have: win a resounding victory in a state that President Trump lost. She has also surpassed a more enduring milestone, having now outlasted Margaret Chase Smith, the first woman to represent Maine in the Senate, to become the longest-serving Republican woman in the chamber’s history…

Ms. Collins said she was open to working with former political foes in order to achieve legislative accomplishments. But having survived a brutal campaign in which Democrats savaged her, Ms. Collins has reason to hold some grudges. She pointedly noted that Senator Chuck Schumer, Democrat of New York and the minority leader, presented “a challenge” given “the millions of dollars in blatantly false ads he ran against me.”…

“It puts her in a very strong position to get things done in the Senate,” said Steve Abbott, her campaign manager and a longtime adviser. He described “a special self-confidence that comes” from “beating the odds,” one that, he added, “strengthens her to the core, to do what she thinks is right.”