WASHINGTON — The Senate Republicans’ push to rewrite the Affordable Care Act suffered an ill-timed setback Thursday, as two centrist Republicans announced plans to offer their own health care plan just as leaders released an updated bill of their own.

The move by Louisiana Sen. Bill Cassidy and Lindsey Graham of South Carolina to debut their health care proposal on CNN moments before Senate Majority Leader Mitch McConnell was set to brief members demonstrated how divided the majority remains in its quest to overhaul former president Barack Obama’s signature health care law.

In a joint interview with CNN Thursday, Cassidy and Graham said that they would take the billions of dollars the federal government now receives in taxes under the ACA and direct that revenue to the states.

“We’re gonna see which one can get 50 votes,” Graham said, referring to the number of Republican senators needed to approve any bill in the Senate, given that Vice President Pence is prepared to cast the tiebreaking vote. “We’re not undercutting him; he’s not undercutting us.”

“I’m trying to get a bill that will lock down Republican governors,” Graham said.

“Our problem has been trying to combine tax reform with replacement of Obamacare,” Cassidy said. “We’re giving the money back to the states. The states can do what they want to do. A blue state can do a blue thing; a red state can do a red thing.”

The surprise announcement just before Senate Republican leaders released a revised health care proposal Thursday that would allow insurers to sell austere plans that do not comply with requirements imposed under the Affordable Care Act.