By Susan Cornwell and Yasmeen Abutaleb

WASHINGTON (Reuters) - Republican U.S. Senate leaders, struggling to keep a seven-year-old promise to end Obamacare, turned their focus on Wednesday to passing a slimmed-down "skinny" repeal measure that would throw the issue into negotiations with the House of Representatives.

The last-ditch effort came as senators voted 45-55 against a straight repeal of Obamacare, which provided for a two-year delay in implementation to give Congress time to work out a replacement. Seven Republicans opposed the measure.

It was the Senate's second failure in 24 hours to repeal the 2010 law popularly known as Obamacare, which expanded health insurance to about 20 million people, many of them low-income. On Tuesday, senators rejected the repeal-and-replace plan Republicans had been working on since May.

The failures underscored the party's deep divisions on the role of government in helping provide access to healthcare as the Senate conducted its second day of a freewheeling debate that could stretch through the week.

Republicans said they were still trying to work out what would be in a skinny repeal, which could simply eliminate mandates requiring individuals and employers to obtain or provide health insurance, and abolish a tax on medical device manufacturers.

Senator John Thune, the No. 3 Senate Republican, said the party was trying to "figure out what the traffic will bear, in terms of getting 50 of our members to vote for things that will repeal as much of Obamacare as possible."

Republicans hold a 52-48 majority in the Senate.

Any Senate legislation would be enough to kick the issue to a special negotiating committee with the House, which passed its own version in May. If that panel can agree on a new bill, the full House and Senate would again have to approve the legislation - a process that could last for months.

"I think people would look at it not necessarily based on its content, but as a forcing mechanism to cause the two sides of the building to try to solve it together," Republican Senator Bob Corker said. "That’s going to be the last chance."

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Senator John Cornyn, the No. 2 Senate Republican, told reporters there was growing support for a slimmed-down approach that would kick the can to negotiators.

"I think there is plenty of agreement," he said.

President Donald Trump, who has been in office for six months, has come down hard on his fellow Republicans for failing to act on Obamacare, something that he had promised repeatedly in his election campaign last year. Some Senate Republicans were growing uncomfortable with the chaotic debate.

"We've got to have a more organized process," Republican Senator Ron Johnson said, noting the skinny repeal would simply delay acting on the core issue. "We just don't have the courage and really the intestinal fortitude to suck it up and ... do this right."

Trump attacked members of his own party who opposed repeal, targeting Lisa Murkowski by name in an early morning tweet on Wednesday. Murkowski - a moderate Republican who was one of two party members who voted on Tuesday against opening debate on a bill to end Obamacare as well as one of a larger number of Republicans who voted against a plan to repeal and replace Obamacare - told MSNBC in an interview that she was not worried about the political fallout.

"Every day shouldn't be about winning elections. How about just doing a little bit of governing around here?" she said.

Healthcare industry organizations are similarly troubled and have urged a more bipartisan effort.

The Blue Cross Blue Shield Association, which represents health insurers across the country, said that if the individual mandate is repealed it must be replaced with incentives for people to buy health insurance and keep it year-round.

The mandate is considered critical to helping to hold down the cost of premiums, because it means that healthy people as well as the sick, who incur high medical costs, buy insurance.

The group also said the government needed to fund subsidies for medical expenses and provide funds to cover high-cost patients.

Anthem Inc, a health insurer with more than 1 million customers in Obamacare individual insurance plans, threatened to further shrink its 2018 market participation because of uncertainty about the government paying for the subsidies that make the plans affordable for millions of Americans.

(Writing by John Whitesides; Additional reporting by Richard Cowan, Amanda Becker and Caroline Humer; Editing by Mary Milliken and Leslie Adler)