* New attempt to repeal Obamacare lacks support
* Three Republicans say they will vote 'no'
WASHINGTON, Sept 26 (Reuters) - Mitch McConnell, the U.S. Senate's top Republican, clung to slim hopes on Tuesday that his party could still dismantle Obamacare, despite not having adequate support for a repeal bill.
Facing the possibility of another failure to make good on their 7-year-old pledge to roll back the healthcare law, McConnell told senators the debate on healthcare would continue.
He said nothing about whether he would bring the repeal bill to a vote, leaving open the option of letting the measure simply die if more firm votes for it cannot be nailed down.
Republicans have vowed for years to get rid of the 2010 Affordable Care Act, or Obamacare, but they are up against a Sept. 30 deadline to pass a bill with a simple majority, or face a much tougher path toward dismantling it.
Senator Susan Collins rebuffed intense lobbying from fellow Republicans and the promise of money for her state when she decided on Monday to oppose - and likely doom - the latest effort to repeal Obamacare.
It was a blow for President Donald Trump who has made undoing Democratic former President Barack Obama's signature healthcare law a top priority since the 2016 campaign and who pressured Collins in a call on Monday.
Republicans hold a slim 52-48 majority in the Senate and at least two other Republican senators, John McCain and Rand Paul, have already rejected the bill.
No votes from McCain, Collins and another Republican, Lisa Murkowski, killed an effort by the Senate to undo Obamacare in July.
While Obamacare extended health insurance to some 20 million Americans, many Republicans believe it is an unwarranted and costly government intrusion into healthcare, while also opposing taxes it imposed on the wealthy.
McConnell opened the Senate on Tuesday by praising the measure, which is sponsored by Republican senators Lindsey Graham and Bill Cassidy. He said it contrasted sharply with Democratic proposals for "single-payer" healthcare.
"It's an important debate for our country," McConnell said. "It's one that will certainly continue."
The Graham-Cassidy bill would take federal money spent on the Medicaid program for the poor and disabled, as well as subsidies to help Americans buy private insurance, and divvy it up to the states in block grants.
One main complaint by opponents of the bill is that it would mean sweeping cuts in funding to Medicaid. (Reporting by Susan Cornwell; Writing by Alistair Bell; Editing by Kevin Drawbaugh and Bill Trott)