As Ohio Rep. Jim Jordan inches closer to securing the speaker's gavel, he has been working to allay concerns from the more establishment wing of the GOP about how his speakership could hinder their ability to raise campaign cash and keep the House majority next year.

Several Republican lawmakers, aides and operatives told CNN they worry Jordan's brand of flame-throwing politics -- and his role trying to help Donald Trump overturn the 2020 election -- could be a liability in key swing districts and turn off major donors.

One GOP fundraiser, who has raised money for past Republican speakers, told CNN that they have vowed not to raise money for Jordan if he becomes the speaker. The fundraiser also said multiple GOP donors have indicated that they wouldn't cut big checks for the party and would rather invest in trying to flip the Senate than take a bet on the House, which they see as a far riskier proposition if Jordan is holding the gavel.

"We're gonna have to pitch to major donors why we're worth investing in," one GOP operative told CNN.

Added a Republican lawmaker who is still on-the-fence about Jordan: "It's a genuine concern he doesn't play well in purple districts."

Jordan has worked to assuage those concerns in private conversations with holdouts, arguing he'll be able to attract more conservative donors who wouldn't have otherwise contributed to the main party apparatus and pointing out that the infrastructure built by former Speaker Kevin McCarthy will still be in place, according to multiple sources familiar with his pitch.

Jordan has also vowed to protect moderates, and some lawmakers believe that having the support of Jordan -- and vice versa -- could insulate them from right-wing primary threats. And in a sign of how that message is playing, Jordan has significantly worn down his opposition over the past 24 hours, including from the moderate wing.

"Mr. Jordan is ready to fundraise for all members of the GOP conference across the country when he's Speaker," a source familiar with Jordan's pitch told CNN.

Some of Jordan's allies have also pointed out that some major donors vowed to stop contributing to the party after the January 6, 2021, attack on the Capitol, but they started coming back around over time.

But Democrats are already preparing for how to frame a Jordan speakership to their advantage going into next year's midterms. The House Democratic campaign arm has been sending out news releases highlighting the House Republicans who represent moderate or swing districts that are backing Jordan.

And a Democratic-aligned outside group, Congressional Integrity Project, launched a new digital ad on Monday in the 18 districts that Republicans represent that President Joe Biden also won, highlighting Jordan's role attempting to help Trump overturn the 2020 election.

The GOP operative worries that if Jordan ascends to the speakership, it could inspire new GOP retirements -- and put more Republican seats in play. The operative also said that even if Jordan can protect vulnerable members from the right, it's an open question of whether he can protect them from the left, which is already salivating over the prospect of Jordan being speaker and Trump being the GOP presidential nominee.

"By tying their political futures to an election-denying, anti-law enforcement, pro-shutdown far-right extremist, these so-called moderates are hand-delivering the DCCC content for campaign ads ahead of next year but, more importantly, they are doing a grave disservice to their country," Democratic Congressional Campaign Committee spokesperson Viet Shelton told CNN.

'We just killed our golden goose'

McCarthy has been a massive fundraiser for the party and has spent over a decade building his political operation and relationships with billionaire donors. His political team recently announced he brought in a record-breaking $78 million for Republicans this cycle.

McCarthy may still be a draw with the donor class, but it's unclear how active he plans to be -- and whether he would still have the same appeal now as a rank-and-file member.

And while the Congressional Leadership Fund, the super PAC aligned with McCarthy, would likely pass on to the next speaker, it's not a guarantee that the relationships -- and donor checks -- would follow suit.

"We just killed our golden goose," one Republican told CNN after McCarthy was ousted as speaker.

CLF, however, put out a memo to donors vowing to remain committed to reelecting Republicans, no matter who is in charge.

"CLF is no stranger to House leadership transitions, as we have been through productive transitions from Speakers Boehner to Ryan to McCarthy, and this will be no different," Dan Conston, the president of CLF, wrote in a memo obtained by CNN. "We will remain a good steward of donor resources and an effective weapon to protect our incumbents and elect standout candidates."

Jordan, though, is popular on the right and has improved his fundraising abilities over the years as he worked his way up through the ranks. Jordan -- who only recently became Judiciary Committee chairman -- has raised more than $14 million this cycle, according to Federal Election Commission data.

But there's some concern in the GOP about Jordan's track record when it comes to his involvement in past elections. The political arm of the House Freedom Caucus, which Jordan has raised millions for, has supported primary challenges to 10 Republican incumbents over the past few cycles.

Jordan, however, has vowed to be a team player and unite the conference if he becomes speaker, and also promised not to let the House devolve into dysfunction under his watch -- a message that has sold some key Republicans.

"His pitch is to ensure that we have a functional government and that we can operate as a conference to move forward," GOP Rep. Derrick Van Orden of Wisconsin, who initially supported House Majority Leader Steve Scalise for speaker but now backs Jordan, told CNN.