(Adds second Republican backing health reform, details)

WASHINGTON, Nov 7 (Reuters) - After a narrow win in the U.S. House of Representatives, President Barack Obama’s fight for a sweeping healthcare overhaul moves to the U.S. Senate where it faces a difficult path to approval.

The Senate’s version of healthcare reform has been stalled as Democratic leader Harry Reid awaits cost estimates from congressional budget analysts and searches for an approach that can win the 60 votes needed to overcome Republican procedural hurdles.

Eventually, the House and Senate will have to reconcile their separate bills into a single proposal that can be signed by Obama, who has set a now-threatened goal of finishing work by the end of the year.

Here is a look at how the issue might play out as it moves through Congress over the next few weeks:

SENATE BILL

Reid has made his toughest decision in merging the separate bills passed by the Finance and Health panels: He included a national government-run public insurance option, which was part of the Health bill but was not in the Finance measure.

Reid also included a compromise that would allow states to decline to participate, or “opt out,” of the government-run program -- an effort to appease moderates, most from conservative Republican-leaning states, who oppose a national public option.

Reid has little margin for error -- Democrats control exactly 60 votes, the number needed to overcome procedural hurdles and pass a bill. Most of the dozen or so Democratic moderates in the Senate remain uncommitted or oppose the public option.

Senator Joe Lieberman, an independent who caucuses with Democrats, opposes the public option and has said he will side with Republicans to block a final vote on any bill that includes one.

Senators Mary Landrieu, Ben Nelson, Evan Bayh and Blanche Lincoln are the other Democrats who appear to be most resistant to Reid’s approach on a public option.

Obama has been meeting lawmakers privately at the White House in an effort to persuade the uncommitted moderates, and Senate leaders have explored possible alternatives that could keep them on board.

One of those could be Republican Olympia Snowe’s favored approach of a “trigger” that would activate a government plan in states where there is not enough competition in the insurance market.

Snowe is the only Republican in the Senate to back one of the healthcare reform bills in a committee vote, but she has said she will oppose a bill with the “opt-out” public option.

A first-term House Republican, Anh Cao of Louisiana, became the second Republican to endorse the healthcare overhaul on Saturday when he backed the House bill.

Reid is waiting for the Congressional Budget Office to provide him cost estimates, and Democrats say a response is not expected until at least late next week.

Reid could be ready to publish the measure and move to floor debate fairly quickly once he gets the estimates, but the Senate will be in recess for a week around the Thanksgiving holiday in late November.

Democratic aides said the bill is likely to drop a mandate that all employers offer insurance to workers or pay a penalty. Differences over the amount of subsidies offered to help lower- and middle-income people buy insurance and on the taxes imposed to pay for the plan must also be overcome.

A floor debate that could last several weeks is now expected to begin in the next few weeks.

CONFERENCE COMMITTEE

Once the Senate and House have passed separate measures, they will appoint negotiators to a conference committee that will negotiate the differences. Their final bill must be passed again by the House and Senate.

It is at this stage where Obama and White House staffers can become most active in closed-door negotiations, cementing what they want in a final bill and what they think is most likely to pass in each chamber.

A final bill would be sent to Obama for his signature, with a goal of finishing work by the end of the year.

Deadlines on the bill have slipped repeatedly, however, and Reid has raised the possibility that final action on the measure could drift into January. (Editing by Arshad Mohammed and Peter Cooney)