A bipartisan group of political operatives — spanning the ideological spectrum from former members of the hard-right House Freedom Caucus to a Democrat who challenged Representative Marjorie Taylor Greene of Georgia — has started a political action committee aimed at “stopping MAGA” and eradicating what the operatives call an authoritarian streak among some Republican lawmakers.

The group, Mission Democracy PAC, will challenge far-right members of Congress in their often deep-red home districts, running ads and messaging campaigns that accuse the politicians of holding antidemocratic and extreme positions.

Mission Democracy PAC begins with just over $500,000 in the bank, but the advisers say they hope to raise $18 million for the coming election cycle, and plan to spend all of it within the targeted congressional districts.

Who’s behind the group? The leaders are former Representative Denver Riggleman of Virginia, who once belonged to the Freedom Caucus but has since left the Republican Party and spoke out against conspiracy theories from the House floor; Olivia Troye, a former official in Donald J. Trump’s administration who has been critical of him; and Marcus Flowers, an Army veteran and Democrat who lost heavily to Ms. Greene last year.

“If we don’t do something now, if we don’t get these extreme MAGA members out of Congress, we stand to lose our very democracy,” Mr. Flowers said in an interview. “It’s time to hold those members accountable, take them to task, attack them in their districts.”

First shots fired. The first ad from the group, a minute-long spot that ticks through several Republican moves to restrict abortion rights, strikingly uses an F-word that is rarely wielded in political advertising.

“Our government is held hostage by a band of politicians so extreme that only the word fascist describes them,” the ad says.

The ad then lists its targets: Ms. Greene, described as “the avatar of these extremists,” as well as Representatives Matt Gaetz of Florida, Lauren Boebert of Colorado, Jim Jordan of Ohio, Scott Perry of Pennsylvania and Paul Gosar of Arizona.

Only Mr. Gaetz’s office responded to requests for comment, pointing to his large margins in victories in past elections and stating that “special-interest PACs aren’t trusted by Floridians — Congressman Gaetz is.”

The group has booked what it describes as a mid-five-figure buy for the ad in Ms. Greene’s district, a relatively small opening salvo.

In an interview, Ms. Troye said the group was focused on defeating “the worst of the worst,” and expected to add more officials to target in the future.

Uphill battle: All of these House members come from heavily Republican districts, and all except Ms. Boebert and Mr. Perry won re-election last year by more than 30 percentage points. (Ms. Boebert eked out victory by 546 votes.) None of them faced a serious threat in their primary elections.

In short, while many Democratic voters dream of toppling these pugilistic Republicans, it is often all but impossible.

Mr. Flowers, for example, raised nearly $17 million in his race against Ms. Greene. She crushed him by 32 points.

But the group argues that pouring money and negative advertising into such races can still weaken politicians: They are forced to spend more time defending their seats, raising money and campaigning at home instead of traveling the country and expanding their political profiles with endorsements and speeches.

There’s always money in the banana stand. In liberal politics, there are few better ways to rake in mountains of cash than by targeting far-right Republicans.

For example, the Lincoln Project, a group of former Republicans that has pumped out stinging ads attacking former President Donald J. Trump and his allies, has raised $118 million since forming in 2019.

The leaders of Mission Democracy expressed confidence in their ability to raise money.

“We’re all pretty prolific with our lists, we know a lot of people to call and we all have pretty good reputations for sticking to facts, not fantasy,” Mr. Riggleman said. “We’ve all had incredibly insane real jobs in the real world. And I just think it’s given us a unique way not only to do the mission, but also fund-raise and get the monies that we need to continue.”