Senate Republicans and the White House pressed ahead Tuesday with their suddenly resurgent effort to undo former president Barack Obama’s signature health-care law, even as their attempt was dealt a setback when a bipartisan group of governors and several influential interest groups came out against the proposal.

Powerful health-care groups continued to rail against the bill, including AARP and the American Hospital Association, both of which urged a no vote. But it was unclear whether the opposition would ultimately derail the attempt, as key Republican senators including Lisa Murkowski of Alaska said they had yet to make up their minds.

The measure marks the last gasp of Republican attempts to dramatically gut Obama’s Affordable Care Act, which has added millions of people to the ranks of the insured through a combination of federally subsidized marketplaces and state-level expansions of Medicaid, leading to record lows in the number of those without health insurance. The Graham-Cassidy bill — named for Sens. Lindsey O. Graham (S.C.) and Bill Cassidy (La.) — would convert funding for the ACA into block grants for the states and would cut Medicaid dramatically over time.

The governors who signed the letter are particularly notable, since some are from states represented by Republican senators who are weighing whether to back the bill. Among the signers were Alaska Gov. Bill Walker (I), who holds some sway over Murkowski, a potentially decisive vote who opposed a previous Republican effort to repeal and replace the Affordable Care Act.