WASHINGTON — Congress’s rush to dismantle the Affordable Care Act, once seemingly unstoppable, is flagging badly as Republicans struggle to come up with a replacement and a key senator has declared that the effort is more a repair job than a demolition.

“It is more accurate to say ‘repair Obamacare,’” Senator Lamar Alexander, Republican of Tennessee and chairman of the Senate health committee, said this week. “We can repair the individual market, and that is a good place to start.”

The struggles and false starts have injected more uncertainty into insurance markets that thrive on stability. An aspirational deadline of Jan. 27 for repeal legislation has come and gone. The powerful retirees’ lobby AARP is mobilizing to defend key elements of the Affordable Care Act. Republican leaders who once saw a health law repeal as a quick first strike in the Trump era now must at least consider a worst case: unable to move forward with comprehensive health legislation, even as the uncertainty that they helped foster rattles consumers and insurers.

Insurers are threatening to exit the Affordable Care Act’s market unless the Trump administration and Congress can quickly clarify their intentions: Will they support the existing public marketplaces, encourage people to sign up and keep federal assistance flowing to insurers, or not?