Republicans finally may be walking back their over-the-top opposition to Obamacare, instead offering tweaks that could make adjustments to current law.

The House has voted more than 60 times to repeal the 2010 Affordable Care Act, President Barack Obama’s signature legislative achievement. Since the law was implemented, 20 million Americans have gained coverage, the Department of Health and Human Services reported in March.

The moves toward compromise come as health insurers have announced hefty premium increases, with BlueCross BlueShield of Tennessee this week announcing a 62 percent increase request. In Georgia, Humana is seeking an average 65.2 percent premium increase.

At the same time, California is poised to open coverage to undocumented immigrants. To do that, however, the state needs permission from the federal government.

The House Energy and Commerce Committee on Friday considered five bills that would make changes like altering the proof needed for coverage and regulating the use of age in setting premiums, the Hill reported. The bills come ahead of Speaker Paul Ryan’s task force plan for replacing the system rather than just repealing it.

But with little time left on the legislative calendar until lawmakers morph into full campaign mode, it is unclear exactly how much can get done, especially in light of Democratic opposition.

Committee Chairman Fred Upton, R-Mich., noted the task force plan won’t actually be put in bill form. Instead it will serve as a “discussion document.”

The Hill reported the House Ways and Means Committee could consider small-scale changes to healthcare taxes next week.

Rep. Gene Green, D-Texas, said he is encouraged by the fact that Republicans finally are holding hearings.

“Let’s go back and fix it, because any bill Congress ever passed, typically we wait a year or two, see how it works, we go back in and fix the problems,” Green told the Hill. “We haven’t had that opportunity because it’s always just: ‘Repeal.’”

The insurance industry lobbying group America’s Health Insurance Plans expressed optimism about the bills, saying members “appreciate … promising strategies for addressing” concerns, including the upward pressure on premiums.

Other industry lobbyists told the Hill they are confused about why Republicans would tweak Obamacare but still talk about replacing it. GOP lawmakers said, however, the actions are more an effort to control premiums.

“This is why we are here today: to offer better care at a fairer price,” Rep. Joe Pitts, R-Pa., said.