House Paul D. Ryan (R-Wis.) speaks during the Friends of Ireland Luncheon at the Capitol on Thursday. (Olivier Douliery / Pool/EPA)

Arch conservatives have come to define the House Republican brand this decade, pushing the Treasury to the edge of default in 2011, shutting down the government in 2013 and supporting the most right-wing contenders in last year’s presidential primary.

Now, however, Speaker Paul D. Ryan (R-Wis.) is dealing with a different rebellious flank within the House Republican Conference as he pushes a massive health-care bill toward the floor next week. Larger in number but softer in tone than their conservative counterparts, moderate Republicans are shaping up to be at least as big a hurdle to achieving the long-held goal of repealing the 2010 Affordable Care Act and replacing it with a more market-oriented series of policies.

These Republicans are getting their share of meetings with Ryan and his leadership team, voicing their concerns about the impact specific pieces of the bill would have in their districts. They are making clear that any negative fallout from these policy moves would place their seats in jeopardy in next year’s midterm elections, a fate that Ryan understands would open the door to losing the House majority.

And, of course, these moderates are making their case in a much quieter fashion than members of the House Freedom Caucus, a group of roughly 30 conservatives who have used their high-profile media appearances to gain several audiences with President Trump to question Ryan’s direction in the health-care fight.

“We have our own way of evaluating things and making our points heard, and it’s not necessarily through the press, the way that they do it,” Rep. Ryan Costello (R-Pa.), a second-term lawmaker from the Philadelphia’s western suburbs, said Thursday.

This is new math for Ryan. In his first year on the job, he mostly faced the same battles that his predecessor, John A. Boehner, had in his five years as speaker: The right wing always caused the most trouble.

Eventually those rabble-rousers from the Freedom Caucus helped push Boehner (R-Ohio) out the door by threatening to oppose his hold on the speaker’s gavel, and they had enough votes to likely block him.

For sure, conservatives far outnumber moderates in the increasingly right-tilting caucus that Ryan oversees. But the vast majority of those conservatives are amenable to Ryan’s policy provisions, leaving 30 or so members of the Freedom Caucus as the biggest troublemakers.

Meanwhile, according to an analysis by the FiveThirtyEight blog, there are roughly 60 Republicans who are either members of the mainstream Tuesday Group or sit in districts that leaned toward Hillary Clinton in the presidential election.

The speaker can afford just 21 defections from his ranks and still pass the bill by the slimmest of margins, so Ryan convened a meeting Thursday with three representatives each from the ideological caucuses, including the Freedom Caucus, the more traditionally conservative Republican Study Group and the moderates in the Tuesday Group.

In the fight over Ryan’s health bill, the American Health Care Act, Republican strategists suggest the members of the far-right corner of the conference do not have enough votes to sink the legislation on their own.

There’s also a particularly strong belief among House GOP leaders that if Trump puts his full force behind the legislation, these Freedom Caucus members will buckle.

Take Rep. Mark Meadows (R-N.C.), the caucus chairman, who is currently leaning against the legislation. Trump won Meadows’s district in western North Carolina by nearly 30 percentage points, a much bigger margin than Republican Mitt Romney won there in 2012.

That’s not the case with almost three dozen Republicans who come from districts that Clinton won or that Trump won by less than 4 percentage points.

These Republicans saw the Congressional Budget Office estimate of 24 million more uninsured from Ryan’s legislation and gasped. They know their constituents might be frustrated with Obamacare, but they tend to be more diverse and from the suburban professional ranks, unwilling to throw people off insurance with no substitute.

“We just need to make sure that we are helping the people who are most in need,” Rep. Carlos Curbelo (R-Fla.) said.

Curbelo won a second term from his South Florida district in a rout even though Trump lost there by 16 percentage points.

But 2018 will be a very different race. Like the vast majority of Republicans in tough districts, Curbelo has never run with a Republican holding the presidency.

Rep. Darrell Issa (R-Calif.), a longtime reliable ally of leadership, also won’t commit to supporting the health legislation despite a meeting Wednesday with Ryan. He barely survived his 2016 election after his suburban Southern California district swung sharply to Clinton.

Many of these wavering Republicans come from states that adopted the expanded Medicaid rolls the ACA allowed, a provision that would be phased out under the current Ryan proposal.

That’s one of the “great concerns” for Rep. Daniel Donovan (R-N.Y.), whose district in Staten Island and Brooklyn actually supported Trump by a wide margin. His meetings with local health industry officials have been brutal.

“They’re all against the current form of the bill, they’re all concerned,” Donovan said.

He wants to prevent his Freedom Caucus counterparts from speeding up the phaseout of the Medicaid expansion.

“Our health-care system is broken, it needs to be repaired, but I think we have to help those people that were harmed by the Affordable Care Act without harming the people that were helped by it,” Donovan said Thursday.

The underlying theme of the Tuesday Group Republicans is to make their voices heard quietly, in the speaker’s office or on the House floor, to try keep the bill from going too far to the right. “You sort of want to keep your powder dry until you’re able to look at everything and sift through it,” Costello said.

Ultimately, however, the test for these Republicans will be how they respond if Ryan and Trump appease the conservatives.

Rep. Charlie Dent (R-Pa.), chairman of the Tuesday Group, delivered a warning that his moderates might be willing to topple the entire legislation if it means a bad deal for their districts.

He wouldn’t commit to how many were in those ranks, but for the first time these moderates have leverage, if they choose to use it.

“Enough to make a difference,” Dent said.

Read more from Paul Kane’s archive, follow him on Twitter or subscribe to his updates on Facebook.