In the plan, the top leaders can serve for only three terms in the majority party and one more term beyond that would require approval by two-thirds of the Democratic caucus instead of the current simple majority.
The proposal also limits the time her two deputies, Minority Whip Steny Hoyer (D-Md.) and Assistant Democratic Leader Jim Clyburn (D-S.C.), can stay in their posts, although those changes will likely have to be ratified by the full caucus.
In an about-face, US Representative Seth Moulton, the Salem Democrat who recently spearheaded an effort to prevent Nancy Pelosi from becoming House speaker, indicated Wednesday he would vote for the California Democrat to assume that post once again.
"I don't think we should have a debate in front of the press on this", Ms Pelosi said, adding: "Let's call a halt to this".
"We wish to thank Nancy Pelosi for her willingness to work with us to reach this agreement", the lawmakers wrote. "As such, I intend to fight alongside my colleagues to make sure the entire leadership team and future leadership teams are bound by this deal", said Pelosi.
"The House Republicans could bring up this bill, if they had the votes, immediately, and set the tone for what you want", Pelosi replied as the president pressed for $5 billion in clearly necessary border wall funding.
To be nominated to a fourth term under the agreement, Pelosi would need to garner a two-thirds majority of House Democrats.
The public display this week points to the return of one of the more powerful leaders in the history of the House, even if she's now term-limited herself to serving as speaker no more than four years.
Pelosi, who is seeking to become House speaker in January, said she and many other Democrats consider the wall "immoral, ineffective and expensive" and noted that Trump promised during the 2016 campaign that Mexico would pay for the wall, an idea Mexico has repeatedly rejected.
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Defeats in Chhattisgarh , Madhya Pradesh and Rajasthan would dent his invincible image and put the party on the back foot. Regional parties - the Telangana Rashtra Samiti (TRS) and the Mizo National Front (MNF) - are leading in these states.
A small group of unhappy Democrats - potentially enough to thwart her drive to win the job - had been threatening to vote against her unless she agreed to limit her service.
"I am very proud to have joined with my colleagues to make lasting positive change to our party".
There are still a handful of Democrats who may not support Pelosi for speaker. With 235 Democrats in the House, she can afford to lose 17 of her own and still get to 218.
Not everyone on the Democratic side is pleased with the turn of events, and Republicans made clear they are more than eager to accommodate Pelosi's rise, employing the kinds of attacks they have for years used against her.
It's still unclear whether the term limits will be officially adopted, as the caucus still has to approve a rule change and many Democrats have already expressed staunch opposition to the idea. During a roundtable with reporters Tuesday, Hoyer chafed at the idea.
If the term limits are adopted, Moulton says it will be better for the party, especially younger members.
Lindsey Graham urged President Trump to "dig in, not give in" after he got into a bust-up with Nancy Pelosi and Chuck Schumer over border security. "Pelosi rebels? No such thing".
"For some time, there have been a number of conversations to advance a proposal to institute term limits for senior leadership positions in our caucus", Pelosi said in a statement announcing her support for the plan.