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 bill — coming two months after a previous failed repeal effort in the Senate — is the subject of a last-ditch lobbying push by Senate Majority Leader Mitch McConnell (R-Ky.) and the Trump administration, led by Vice President Pence, ahead of a Sept. 30 deadline for Senate action.

In a letter to Senate leaders, the group of 10 governors argued against the Graham-Cassidy bill and wrote that they prefer the bipartisan push to stabilize the insurance marketplaces that Sens. Lamar Alexander (R-Tenn.) and Patty Murray (D-Wash.) had been negotiating before talks stalled Tuesday evening.

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.

Nevertheless, Murkowski said Tuesday afternoon that she was still weighing her options and explained how her position on the bill might ultimately differ from her opposition to the repeal effort that failed dramatically in July.

“If it can be shown that Alaska is not going to be disadvantaged, you gain additional flexibility. Then I can go back to Alaskans, and I can say, ‘Okay, let’s walk through this together.’ That’s where it could be different,” she said.

But Murkowski, who has been in close contact with Walker, said she did not yet have the data to make such a determination. Alaska’s other Republican senator, Dan Sullivan, said he was still mulling whether to support the bill.

On the other side, a group of 15 Republican governors announced their support for the Senate bill Tuesday evening. The list includes Kentucky Gov. Matt Bevin (R), whose backing could help influence Sen. Rand Paul (R-Ky.), who has frequently criticized the legislation for failing to fully repeal the ACA.

On Tuesday, Pence traveled from New York, where he was attending the annual United Nations General Assembly session, to Washington with Graham in a sign of the White House’s support for the proposal.

“My message today is I want to make sure that members of the Senate know the president and our entire administration supports Graham-Cassidy,” Pence told reporters on the flight. “We think the American people need this.”

Graham added that President Trump called him at 10:30 p.m. Monday.

“He says, ‘If we can pull this off, it’ll be a real accomplishment for the country,’ ” he recalled.

Trump has played a limited role in building support among senators in recent days, but it is possible that his participation will increase as a potential vote nears. He has, however, been in touch with some governors, including a weekend call with Arizona Gov. Doug Ducey (R), according to aides.

Pence attended the weekly Senate Republican policy luncheon, where he said the current health-care system is collapsing and the bill fulfills key GOP promises to return control to states and rein in federal entitlement programs, according to several GOP senators.

Afterward, McConnell declined to ensure a vote on the bill but said his team is working to secure sufficient support.

“We’re in the process of discussing all of this. Everybody knows that the opportunity expires at the end of the month,” said McConnell, referring to the limited window Republicans have to take advantage of a procedural tactic to pass a broad health-care bill without any Democratic support.

Democrats say the ACA needs modest improvements by Congress but is working well overall, and they have railed against a process in which Republicans are pressing ahead with few hearings on legislation that would affect an industry that accounts for about a sixth of the U.S. economy.

The current bill would give states control over billions in federal health-care spending and enact deep cuts to Medicaid. The Medicaid cuts in particular are a major source of concern to the governors, both in terms of imposing a per capita limit on what states would receive and putting restrictions on how they could spend any federal aid on their expanded Medicaid populations.

Medicaid was expanded under the ACA to provide states with generous funding if they opted to cover adults earning up to 138 percent of the poverty level. Many Republican-led states decided against an expansion following a Supreme Court decision allowing them to opt out.

The fact that the bill also would restrict states’ abilities to tax health-care providers to fund their Medicaid programs posed a problem for several governors, as well.

In a sign of how alarmed state officials are about the prospect of funding cuts, Louisiana’s health secretary sent a letter to Cassidy on Monday saying that their state could see disproportionate cuts with significant impacts on people with preexisting or complex and costly conditions.

"This would be a detrimental step backwards for Louisiana," wrote Rebekah Gee, who posted her letter on Twitter on Monday.

And although Walker has not played a visible role in the national health-care debate until now, certain aspects of the new bill pose an even bigger challenge for Alaska than previous proposals did. Health-care premiums are particularly expensive in the state, given its many remote areas. Premiums on the ACA market average roughly $1,000 a month for an individual, according to the most recent federal data.

Since federal tax credits over time would be equalized and based on the number of low-income people in a given state, that new calculation would eliminate the more generous subsidies Alaska enjoys.

Given the complex nature of the Graham-Cassidy proposal, it is difficult for state officials and health-care analysts to predict exactly how much money a given state would gain or lose if the legislation were enacted. But early estimates suggest that states with expanded Medicaid programs and active participation in the ACA markets could face major cuts.

An initial estimate for Colorado, according to state officials, suggests it could lose at least $700 million in annual federal funding by 2025. Since the state has roughly 450,000 people in its Medicaid expansion program and another 100,000 receiving premium tax credits on its health-care exchange, that could translate into hundreds of thousands of Coloradans losing coverage.

The governors who have been most outspoken in their criticism of the bill negotiated behind the scenes to bring as many state executives on board as possible, according to aides, tweaking the language of Tuesday’s letter over the past couple of days to get maximum support.

Others who signed the letter in opposition to Graham-Cassidy included John Kasich (R-Ohio) and Brian Sandoval (R-Nev.). Sandoval’s positioning puts him at odds with Sen. Dean Heller (R-Nev.), who has been touting the bill as another co-sponsor.

Pence said Trump told him to reach out to some Democrats, and he spoke to Sen. Joe Manchin III (D-W.Va.) over the weekend. But after reviewing the bill, Manchin said, he told Pence’s aides he could not support the legislation.

Senate Minority Leader Charles E. Schumer (D-N.Y.) said he’s confident no Democrat will vote for the legislation, because “it hurts people in every state.”

Democrats had been working furiously since Monday to advance talks between Alexander and Murray on a deal to immediately stabilize ACA insurance marketplaces with federal subsidies. The negotiations rapidly escalated after weeks of slow but consistent talks once it became clear that Senate GOP leaders were serious about holding a health-care vote before the end of the month, according to several Senate aides.

Alexander on Tuesday played down expectations of reaching an agreement this week, telling reporters the pair had reached an impasse.

"During the last month, we have worked hard and in good faith but have not found the necessary consensus among Republicans and Democrats to put a bill in the Senate leaders' hands that could be enacted," Alexander said in a statement.

Democrats denied that the talks had fallen apart, accusing Republicans of walking away despite making progress on areas of disagreement. Schumer spokesman Matt House said Democrats offered to accept a number of GOP requests, including waivers to give states more latitude in how they spend federal dollars and the creation of new low-cost plans under the ACA.

“This is not about substance,” House said in a statement. “The Republican leadership is so eager to pass Graham-Cassidy that they’re scuttling a balanced, bipartisan negotiation.”

Many Democrats, including Murray, said they hoped the talks could still be salvaged despite roadblocks from Republicans.

"I am disappointed that Republican leaders have decided to freeze this bipartisan approach," Murray said in a statement. "But I am confident that we can reach a deal if we keep working together."

Ed O’Keefe and Ashley Parker contributed to this report.