But inside the West Wing, President Biden has made it clear that he is uncomfortable even using the word abortion, according to current and former advisers. In speeches and public statements, he prefers to use the word sparingly, focusing instead on broader phrases, like “reproductive health” and “the right to choose,” that might resonate more widely with the public.

Mr. Biden, a practicing Catholic who has drawn on his faith to shape his political identity, is now being called on to lead a fight he spent decades sidestepping — and many abortion rights advocates worry that he may not be the right messenger for the moment.

Once an outright critic of abortion rights and later a committed but quiet defender of them, Mr. Biden has a history that gives activists pause.

“This is not necessarily the guy that I am sure most activists wanted in the seat when this happened,” said Jamie L. Manson, the president of Catholics for Choice, referring to the court’s decision overturning Roe v. Wade. “It’s unfortunate because he has so much power and we need him to really get out of his comfort zone.”