Although she easily won the nomination, Ms. Pelosi’s victory carried notes of caution for a leader who has proclaimed unequivocally that she had the votes to become speaker. Those who have pressed for a new leader have long believed that after they showed she did not have such support, they could force a debate over an alternative candidate for speaker, a clear time limit on her tenure or a compromise in other leadership posts that would ensure a generational change at the top — all options Ms. Pelosi has refused to consider.

But Ms. Pelosi, who excels at legislative haggling and the corralling of a sometimes fractious group of Democrats, has demonstrated in the past that she has the capacity to win over dissenters with a mix of sweeteners and unspoken threats. The last time she faced opposition, when Mr. Ryan challenged her for minority leader in 2016, she lost 63 Democrats, almost twice the number that voted against her on Wednesday.

Her deal with the Problem Solvers Caucus appeared to ease her path considerably. Among the changes she agreed to were one that would make it easier for “consensus” bills — those that gain at least 290 co-sponsors — to get a vote on the House floor, and for bipartisan amendments, with at least 20 members of each party supporting them, to be considered in committees.

Another notable change would eliminate the ability of one member to essentially force a vote of no confidence in the speaker, a threat that has allowed the House Freedom Caucus, a group of ultraconservative Republicans, to handcuff the speaker, and ultimately led to the resignation of Speaker John A. Boehner in 2015. Instead, the move would have to be initiated by a party caucus or conference.