“While this legislation does not fully repeal Obamacare, it’s an important step in keeping that promise to lower healthcare costs,” the Freedom Caucus said in its statement upon passage of the AHCA. It was a message echoed by outside groups like FreedomWorks, Heritage Action, and the Club for Growth, who agreed to drop their opposition to the bill, a move that gave Republicans additional cover to vote for it. Conservatives had embraced an incrementalist approach to Obamacare. The new standard they adopted for health-care legislation was not whether it eliminated the Affordable Care Act but whether it would lower premiums for most consumers.

One key question for McConnell is whether the most outspoken conservatives in his caucus—Senators Rand Paul of Kentucky, Ted Cruz of Texas, and Mike Lee of Utah—will judge the Senate bill by that more modest baseline. Republicans can lose no more than two votes to secure passage, and a group of moderate senators is proving just as difficult for party leaders to nail down. To this point, Paul has been the most critical of the GOP approach and the most likely to oppose the proposal from the right. The House bill, he complained, already kept 90 percent of Obamacare’s subsidies. “If this gets any more subsidies in it, it may well be equal to what we have in Obamacare. So it really wouldn’t be repeal,” Paul said on Tuesday, according to Bloomberg. Even so, the Kentucky conservative wouldn’t rule out supporting the bill until he read the text.

Cruz and Lee have participated in the Senate process as members of the 13-man working group, and aides have said both have bought into McConnell’s incremental approach. But the two have each complained about the emerging draft in recent days, either on the substance or the top-down, secretive process used to write the bill. “We’re not there yet,” Cruz said Tuesday on Fox News. “The current draft doesn’t do nearly enough to lower premiums.”

The Congressional Budget Office projected that in states that opted out of Obamacare’s insurance requirements under the waivers allowed in the House bill, average premiums would drop significantly. But the tradeoff is that people with preexisting conditions would face sharply higher costs or be priced out of insurance entirely. Conservatives have argued that the high cost of adhering to the ACA’s minimum coverage requirements has forced insurers to raise premiums in order to make a profit.

Conservative activists briefly held out hope that the health-care bill would move further to the right in the Senate, buoyed by efforts by Cruz and Lee to have Republicans override parliamentary rulings limiting how much of Obamacare they could repeal through the budget reconciliation process. But party leaders never seriously considered that option, which moderate Republicans were likely to oppose.