WASHINGTON - A health reform bill with a government-run insurance option faced an uncertain future in the Senate on Tuesday, with many centrist Democrats uncommitted and Senator Joe Lieberman strongly opposed.

Senate Democratic leader Harry Reid's decision to include a government-run public option in the Senate's bill failed to sway about a dozen moderates who said they wanted more details before making their decisions.

Democrats said Reid was still short of the 60 votes needed to overcome procedural hurdles and pass a bill with a public option, which has become one of the most contentious issues in the debate on President Barack Obama's top domestic priority.

The healthcare bills in the Senate and the House of Representatives aim to rein in health costs, expand coverage to millions of uninsured and bar insurers from denying coverage for pre-existing conditions or dropping coverage for the sick.

Health insurer stocks rallied on Tuesday on skepticism a government-run plan seen as detrimental to the industry would win passage, a view fueled by Lieberman's comments.

Lieberman, an independent who caucuses with Democrats, said he would not join Republicans on a procedural vote to block the healthcare bill from coming up for debate, but would be willing to block a final vote on the plan if it remained unchanged.

I don't support a government-operated health insurance company that will end up costing the taxpayers a lot of money, he told reporters.

SOME DEMOCRATS STILL ON THE FENCE

Senator Olympia Snowe, the only Republican to support a healthcare bill in a congressional committee, opposes the public option and said she would vote with her fellow Republicans to block a motion to proceed to debate on the bill.

Once you put in a motion to proceed, then it's very difficult to change it, she told reporters.

Democrats cannot afford to lose the support on healthcare of any of their members in the Senate where they control 60 votes. As a result, they must woo about a dozen uncommitted moderates.

I'm skeptical about what Senator Reid has proposed. I have not been a supporter of a national government-run option, but I am going to stay open to principled compromise, Democratic Senator Mary Landrieu said.

After days of closed-door negotiations to merge two pending healthcare bills into one for floor debate, Reid said on Monday he would include a national government-run insurance option that would let states opt out of participation.

Reid, Obama and congressional liberals have backed a public option as a way to create choice and competition in the insurance market, but critics call it a government takeover that would hurt the private insurance industry.

Every person has to decide for himself or herself how they are going to vote. For me, it is just too early, Democratic Senator Ben Nelson told reporters.

This is just the next step, there are many more steps and many more opportunities to bring people together, said Democratic Senator Kent Conrad, whose proposal for nonprofit cooperatives to compete with insurers also is included in the Senate bill.

HOUSE LIBERALS HEARTENED

Democratic Senator Tom Carper, who proposed a public option that would let states opt in on participation, said he still thought there was a chance a compromise plan could win approval.

At the end of the day my hope is that we can come up with something that is not only good policy but can get 60 votes, Carper told reporters.

Reid's decision on Monday encouraged liberal Democrats in the House, who are negotiating a merger of three pending healthcare reform bills that all include a public option. They are still trying to compile the 218 votes necessary to pass the strongest version.

Senator Reid's very welcome decision has really lifted us, said Representative Robert Andrews. The consensus now is there will be a public option, the question is what it will look like.

House leaders said they hoped to unveil their bill in the next few days, with a floor debate possibly starting late next week.

The timetable in the Senate is even more unclear. Reid has sent the bill to the Congressional Budget Office for cost estimates, with a response not expected quickly.

The S&P Managed Health Care index of large U.S. health insurers rose 4.24 percent on Tuesday amid a slight decline for the broader market and following a 2.5 percent drop for the index on Monday.

(Additional reporting by Tom Ferraro; Editing by Xavier Briand)