Democratic Leader Nancy Pelosi announced Wednesday evening that she struck a deal with a group of seven rebel Democrats to limit the terms of senior Democratic leaders, paving the way for her election as House Speaker in January.

If the deal is approved by the Democratic caucus, members will be allowed to serve in senior leadership positions for three terms, with an option of a fourth term if they have the support of two-thirds of their fellow Democratic lawmakers. It will retroactively apply to the two leadership terms she and her counterparts, Minority Leader Steny Hoyer, D-Maryland, and Assistant Democratic Leader Jim Clyburn, D-South Carolina, served from 2007 to 2011. That would allow them to serve as House Speaker, majority leader and majority whip for a maximum of four more years.

To become an official rule, the Democratic caucus will have to give their approval. In a statement, Pelosi said she expects it to come up for a vote on February 15, but that she is "comfortable with the proposal" and intends to abide by it whether it passes or not.

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"Over the summer, I made it clear that I see myself as a bridge to the next generation of leaders, a recognition of my continuing responsibility to mentor and advance new Members into positions of power and responsibility in the House Democratic Caucus," Pelosi said in a statement.

She will likely face stiff opposition from Hoyer, the number two leader. During a roundtable with reporters Tuesday, Hoyer chafed at the idea.

"I am against term limits because I have a term limit. It's a two-year term limit. And every year, the citizens that I represent and the members in this House have to re-up my contract," he said.

"She's not negotiating for me," he added.

In the last few weeks, Pelosi has whittled away her naysayers with individual deals and convinced enough of them to support her candidacy for speaker when the House votes on January 3rd.

Rep. Ed Perlmutter of Colorado represented a group of more than 20 Democrats who oppose Pelosi in negotiations over her future. The group, which comprises current members as well as incoming freshmen who were elected on Nov. 6, have called for new leadership in the Democratic Party. Pelosi had resisted the idea of placing an end date on her speakership out of concern it would make her a lame duck before she even took the gavel.

"[Pelosi] has serious support," Perlmutter told CBS News in an interview after the announcement. "And over these conversations I've had with her -- and really I knew this anyway -- but she's just very professional, very competent, and is a serious leader that I think will do a good job for us."

Perlmutter said the decision to wage an intraparty leadership fight was not personal.

"This was not any type of gripe against Nancy Pelosi. She's only supported me. She's only assisted me," Perlmutter said.

The seven Democrats who have agreed to support Pelosi are Tim Ryan of Ohio, who challenged Pelosi in the 2016 congressional leadership elections, Linda Sanchez of California, Bill Foster of Illinois, Seth Moulton of Massachusetts and Filemon Vela of Texas.

Asked about accusations that the Pelosi opposition group was being sexist, Perlmutter said it was "absolutely not" the case.

"You know...these kinds of elections are personal," Perlmutter replied when asked if he had any regrets about perceptions that the group's effort had been a personal attack on Pelosi. "I'm glad we came to agreement because she is a friend of mine," he added.

There are still a handful of Democrats who may not support Pelosi for speaker. And it's far from certain a widespread group of Democrats will vote to impose term limits on Hoyer and Clyburn.

"It just doesn't make sense. If we don't like somebody, then don't vote for them, but to just put an arbitrary term limit on a position I think is just unfortunate," said Rep. Cedric Richmond, D-Louisiana, the outgoing chairman of the Congressional Black Caucus.

"I think that this whole, these guys needing something so that they can land this damn plane is getting silly. Land the plane, vote for her, and let's please get in with trying to raise the minimum wage or something," he added.

Ed O'Keefe contributed reporting