Washington (CNN) The calls from wealthy Democratic donors, influential party bosses and long-time supporters alike are coming in this week to Rep. Kathleen Rice, the New York Democrat who's trying to mount a coup against Nancy Pelosi.

Rice, who's helping to lead a faction of roughly 18 Democrats who say they won't support Pelosi, is getting a small taste of the furious onslaught waged by Pelosi and her allies to lock down support, limit defections and ensure that she will once again reclaim the speaker's gavel she first wielded more than a decade ago.

The growing pushback on her staunchest foes is the latest sign of how Pelosi is using power she's amassed through her more than three decades on Capitol Hill to once again reclaim her perch atop the House.

On Wednesday, the House Democratic Caucus voted 203-32 at a closed-door meeting to nominate Pelosi as their nominee to be House speaker. While it was an overwhelming majority, she will need to peel off more than a dozen no votes over the next five weeks if she wants to win with 218 supporters on the full floor vote in January, though depending on who votes and how that threshold for victory could be lower.

Even before the vote, anger was mounting at the anti-Pelosi faction, something bound to intensify after Wednesday if the rebels don't fall in line once Pelosi is formally nominated as her party's choice to be speaker next Congress.

"She'll be our speaker," said Rep. John Garamendi of California. "End of discussion."

Pelosi wrangles votes in speaker bid

Despite lacking the votes so far to win a floor vote among the entire House, Pelosi allies have reason to be confident. Roughly 45 surrogates made calls on her behalf. Democratic stalwarts like Al Gore and John Kerry have urged members to fall in line. And she's made many offers they can't refuse -- from perches on key committees to promises to move on legislation they've supported to simply listening to the concerns of her members.

For example, Rep.-elect Ayanna Pressley of Massachusetts told CNN she decided to support Pelosi after being promised a position on the gun violence task force.

"What I care about is that we are leading on those issues that are consequential to the American people," Pressley said. "And the issue that was a priority to me is that we would be moving early in the session on a robust gun bill. And I got that commitment. I've been appointed to the gun violence task force."

Rep.-elect Colin Allred from Texas has still not announced how he will vote on Pelosi, but told CNN that it comes down to what Pelosi can offer him, though he declined to give specifics.

The confidence also comes as the anti-Pelosi faction have struggled to swiftly bring down the California Democrat. The critics so far don't have a candidate who will run against her; Rep. Marcia Fudge, originally part of the group, backed down after Pelosi rewarded her with a spot running a subcommittee.

One member, Rep. Brian Higgins of New York, reversed course and said he'd support her after winning promises -- over the course of three days of phone calls -- to bring up a bill to expand Medicare eligibility and another to spend $1 trillion on infrastructure projects. And others who have held out have found themselves on the phone repeatedly with Pelosi ahead of Wednesday's caucus vote.

"I've voted for you, and I've voted against you," Rep. Jim Costa of California said he told Pelosi in recent days. "And I'd like to support you. I'd like to."

Others signaled a likelihood to support Pelosi because there's no one else who has stepped up.

"I was hoping that someone else would stand up and say, 'Listen, I think I have what it takes to do this as well,'" said Rep.-elect Jahana Hayes of Connecticut, who vowed to oppose Pelosi during the campaign but is now supporting her. "And I didn't see that."

For their part, aides and members in the anti-Pelosi group argue the arm-twisting won't deter the group's ultimate goal of blocking Pelosi from getting the votes she needs on the House floor in January.

Rice argued such "backroom deals represent the establishment-based transactional politics that the American people hate and patently rejected on Election Day."

"These tactics also stifle fair and open leadership elections within our caucus and perpetuate the leadership stagnation that has plagued our party for over a decade," she added.

Anti-Pelosi group eyes January as the end goal

In private conversations over the last several days, Pelosi critics have not been pleased by recent developments, questioning their decision to write a letter that said they were "committed" to voting for new leadership, language that allowed some members to wiggle out of their promises. Now, they believe they can still derail her if she can't get the votes on the floor, something they hope could convince a dark horse candidate to run.

Pelosi's nomination on Wednesday is more of a formality, they said.

"Leader Pelosi will likely win the majority of votes," Rice said Tuesday. "The only number that really matters is 218, and after today it will become clear that she does not have the votes."

Rep. Tim Ryan, who ran against Pelosi for Democratic leader and lost after the 2016 elections, suggested Tuesday night that a challenger might emerge during the caucus vote Wednesday.

"We're going to find out tomorrow," Ryan said when asked if he believed the anti-Pelosi effort has been going well.

The tension highlights an intra-party divide over who should hold the reins as House Democrats take back the majority for the first time since they lost it eight years ago. On one side is the vast majority of the Democratic caucus that's lining up behind Pelosi. On the other side is a tiny faction of members who argue Pelosi's been No. 1 for too long, and it's time for change.

In between are a few dozen Democrats who aren't clearly saying how they plan to vote. Pelosi only needed a majority of the Democratic caucus on Wednesday to win the nomination, but in January she'll need a majority of the full House -- traditionally 218 votes.

A floor fight would lead to "mutually assured destruction" for Democrats on the first day of the new Congress, warned Illinois Democratic Rep. Raja Krishnamoorthi.

"A floor fight while the world is watching would make this the most highly rated swearing in for the wrong reasons," Krishnamoorthi told CNN. "And I think it would lead to us losing the majority potentially on the first vote of a new Congress."

Democrats could have as many as 235 seats in the next Congress, meaning Pelosi can afford to lose only 17 Democrats, if all members vote for a specific candidate. She could win with fewer than 218 votes under certain scenarios.

"It doesn't seem like there's an alternative as part of their strategy," said Rep. Cheri Bustos, an Illinois Democrat, who acknowledged that some Pelosi critics reached out to her to urge her to consider running for speaker.

Negotiating a solution?

Meanwhile on Tuesday, a separate group of six Democrats part of the so-called Problem Solvers Caucus, met for 90 minutes with a top Pelosi confidante, Rep. Jim McGovern of Massachusetts, to try to cut a deal over several rules changes.

The group's proposals would make it easier for rank-and-file members to get bipartisan bills considered by the leadership. Nine Democrats from that group had threatened to withhold their votes until Pelosi backed their calls for changes, but several say they are closer to endorsing her.

"We're that close," said Rep. Tom Suozzi, a Democrat of New York, showing an inch between his thumb and index finger. "It's looking good."

On Wednesday, the problem solvers Democrats put out a statement saying that they had reached an agreement with Pelosi that would "help break the gridlock" in Congress.

While the separate anti-Pelosi group is still determined to keep pushing for leadership changes, they're also signaling openness to possible negotiations with Pelosi -- with the aim of establishing a clear succession plan at some point within the next two years of her term.

Negotiations, however, haven't begun, and there's no clear sign yet the Pelosi would engage with the rebels on that front.

In private conversations with Democratic members, Pelosi has not said when she might step aside or who she favors to replace her.

Asked if the Pelosi critics should drop their efforts if they lose the Wednesday vote, as expected, Rep. Ted Lieu said: "My preference is they should."

One of the most vocal rebels, Rep. Seth Moulton, alluded to that openness of broader talks with Pelosi earlier this week. Given his fraught relationship with Pelosi, it's unlikely the Massachusetts Democrat would be at the forefront of any talks. Rather, there are a few in the group who are still in good standing with the Democratic leader, like Rep. Ed Perlmutter, who some feel could potentially emerge as a lead negotiator if Pelosi agreed to talk.

Pelosi has met with many of her critics, including incoming freshmen Democrats like Max Rose of New York, but she has not spoken to foes like Democrat Kurt Schrader of Oregon.

"Has she talked to me, Kurt Schrader? No," he said. "It should concern her -- not me."

This story has been updated to include Wednesday's developments.