* "We have 12 days to pass it" - Pence
* Bill has momentum, but fate still unclear (Adds failure of separate bipartisan effort to stabilize insurance markets)
By Susan Cornwell and Amanda Becker
WASHINGTON, Sept 19 (Reuters) - The Trump administration and top U.S. Senate Republicans pushed on Tuesday for action on a bill to dismantle Obamacare, but time was running out and they were still hunting for the votes needed to pass their latest attempt to gut the 2010 healthcare law.
Vice President Mike Pence lunched with Republican lawmakers on Capitol Hill to urge them to approve the legislation introduced last week by Republican Senators Lindsey Graham and Bill Cassidy. Pence said President Donald Trump backed the bill.
"Now is the time. We have 12 days" to pass it, Pence said.
The sudden momentum for the Graham-Cassidy bill put the brakes on a separate effort to try to stabilize Obamacare insurance markets. Republican Senator Lamar Alexander said on Tuesday that a bipartisan plan aimed at shoring up the system had failed.
Senate Majority Leader Mitch McConnell, who fell a single vote short of securing passage of another healthcare overhaul bill in July, said the Graham-Cassidy legislation "has a great deal of support," but would not commit to bringing it to the Senate floor for consideration.
After Sept. 30, the last day of the fiscal year, procedural rules will make it much more difficult for Republicans. The bill after Oct. 1 would need 60 votes in the 100-seat Senate to be brought up for consideration, rather than a simple majority until the end of the month.
Despite controlling both chambers of Congress and the White House, Republicans this year have failed to make good on their seven-year effort to dismantle a law that was the top legislative achievement of Trump's Democratic predecessor, Barack Obama.
Dismantling the Affordable Care Act, known informally as Obamacare, was a central campaign promise last year by Trump. Republicans call Obamacare a government overreach into the healthcare system. Democrats point out that it has expanded health insurance coverage to some 20 million people.
The new bill could give Republicans one last shot this year on healthcare.
It proposes to replace Obamacare with a system giving states money in block grants to run their own healthcare programs. It would allow states to opt out of certain Obamacare protections for consumers and waive regulations requiring insurers to cover certain health benefits. It also would end the Obamacare expansion of the Medicaid insurance program for the poor and disabled.
The American Medical Association and American Hospital Association panned the bill, saying it would mean millions would lose health insurance coverage. The American Association of Retired People said it would hike costs for older people and urged Congress to work on stabilizing Obamacare insurance markets, as proposed in the bipartisan package.
Democratic Senator Patty Murray blamed the failure of that effort on the push for the Cassidy-Graham bill. "I am disappointed that Republican leaders have decided to freeze this bipartisan approach and are trying to jam through a partisan Trumpcare bill, but I am confident that we can reach a deal if we keep working together," she said in a statement.
Fifteen Republican governors said on Tuesday they supported the Cassidy-Graham bill. Despite signs of momentum for the legislation, its fate is unclear.
Having suffered humiliating failure in July, Republican congressional leaders only want to hold a vote on legislation they know can pass. Graham would not say how many committed votes he had in a Senate that his party controls 52-48.
Several Republicans, including the three senators whose "no" votes blocked the earlier bill in July, are still undecided, including Graham's close friend John McCain.
A bipartisan group of 10 governors wrote a letter to Senate leaders asking them not to consider the Cassidy-Graham bill.
Alaska Governor Bill Walker was among those who signed the letter. One of his state's two senators, Republican Lisa Murkowski, is among those undecided on the Cassidy-Graham bill.
The clock is ticking. The Senate will not be in session Wednesday through Sunday. The Senate Finance Committee said it would hold a hearing on the bill next Monday.
Graham said House of Representatives Speaker Paul Ryan had told him that if the Senate passed the Cassidy-Graham bill, the House would too.
Trump's administration has repeatedly threatened to cut off payments made directly to insurers, called cost-sharing reductions, that help cover out-of-pocket medical expenses for low-income consumers. It faced a deadline on Wednesday to make the payments for the month of September, and insurers expected to receive the payments.
If the Cassidy-Graham bill were to pass, it would likely affect revenue at most insurers, including small companies like Centene Corp and Molina Healthcare that focus on Medicaid, and larger more diversified companies like Anthem Inc , Aetna Inc and UnitedHealth Group, Wall Street analysts said.
Aetna shares were off 3.1 percent on Tuesday and UnitedHealth was down 1.8 percent, while the stocks of hospital chains were also lower on the possibility of less government funding, including HCA Healthcare’s, down 1.8 percent. (Additional reporting by Richard Cowan and Yasmeen Abutaleb in Washington and Caroline Humer in New York; additional writing by Roberta Rampton; Editing by Will Dunham and Peter Cooney)