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The battle over health care reform has only just begun.

After an overhaul package that was months in the making cleared a major hurdle Tuesday, Senate Majority Leader Harry Reid and House Speaker Nancy Pelosi now must grapple with stiff Republican opposition and warring factions among Democrats as they try to bring an acceptable bill to the floor.

The Senate Finance Committee voted 14-9 to send its version of reform legislation to the Senate floor, becoming the last of five panels to act on legislation and marking the biggest advance so far toward health care reform.

But President Obama previewed the tough road ahead, even as he hailed the vote as a "critical milestone" late Tuesday and pledged to "get this done."

"We have a lot of difficult work ahead of us. There's still significant details and disagreements to be worked out over the next several weeks," Obama said. "We are now closer than ever before to passing health care, but we're not there yet -- now's not the time to pat ourselves on the back."

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In an opening shot of the fight to come, Sen. Bill Nelson, D-Fla., told FOX News that he and his colleagues will push for a controversial government-run health insurance plan to be inserted into the bill.

"When we get to the floor, we're going to try to get that public option," he said, urging "patience" among supporters. "The Majority Leader Harry Reid's going to have to be Houdini. He's going to have to cobble the votes together."

The Finance Committee was the only panel to take out the so-called "public option," replacing it with a system of nonprofit cooperatives. But that bill must be merged with the more liberal version passed by the Health, Education, Labor and Pensions Committee, which includes the public plan, before it hits the Senate floor.

And any attempts to push for the return of the public option are sure to draw heavy fire from moderate Democrats as well as all Republicans.

Sen. Olympia Snowe, R-Maine, the only Republican to back the Finance Committee bill Tuesday, said after the vote: "I can't vote for a public option."

She, along with moderate Democratic Sen. Blanche Lincoln, D-Ark., warned Tuesday that support for the Finance Committee bill does not guarantee support for the final product.

The House still needs to bring its unified version to the floor, and Reid will begin working with White House staff, Finance Committee Chairman Max Baucus, D-Mont., and others to blend the Finance bill with the more liberal version. White House Chief of Staff Rahm Emanuel is headed to Capitol Hill Wednesday to start talks with Democratic leaders on the health care bill.

Even if both chambers can settle on a unified bill, the legislation would then need to go to a conference committee to reconcile differences between the House and Senate before heading to the president's desk. Pelosi has been more forceful in the call for a public option than Reid -- and it's unclear who would prevail if push came to shove. Possible tension between the two seemed to play out last week, when Pelosi edged away from Reid at a press conference as he put his hand on her shoulder.

Senate Republicans made clear after the committee vote Tuesday that they intend to fight the bills in their current form. All 13 Democrats on the panel voted in favor of it, while all Republican except Snowe opposed it.

"It's going to cost us an arm and a leg," Sen. Orrin Hatch, R-Utah, said. "The costs of this are astronomical."

The Finance Committee's top Republican, Chuck Grassley of Iowa, gave voice to the GOP's concerns about the bill, saying it was "moving on a slippery slope to more and more government control of health care."

But Democrats like Nelson intent on the public option will continue to run up against other factions in their own party, let alone GOP resistance.

Sen. Jay Rockefeller, D-W.Va., who wants nothing short of a government-run insurance plan, said Tuesday that while he was voting for the Finance Committee bill he still sees a public option as critical.

"The insurance industry does not know how to stop itself. They are a train which just gathers speed, and with no impediments," he said.

The public option is seen as a way to keep insurance industry costs in check and expand coverage, but the insurance industry staunchly opposes it. Many fear the government option could drive a bulk of the private plans out of existence.

It is just one element of health care reform, but has emerged as the most contentious.

The Baucus plan would, for the first time, require most Americans to purchase insurance and it also aims to hold down spiraling medical costs over the long term. Questions persist about whether it would truly provide access to affordable coverage, particularly for self-employed people with solid middle class incomes.

One of the biggest unanswered questions is whether the legislation would slow punishing increases in the nation's health care costs, particularly for the majority who now have coverage through employers. The insurance industry insists it would shift new costs onto those who have coverage.

Congressional Budget Office Director Douglas Elmendorf, under questioning by Republican senators, acknowledged that the bill's total impact on the nation's health care costs is still unknown. The CBO has been able to establish that the legislation would reduce federal government deficits, but Elmendorf said his staff has not had time to evaluate its effects on privately insured people. Government programs pay about half the nation's annual $2.5 trillion health care tab.

The 10-year, $829 billion Finance Committee bill includes consumer protections such as limits on copays and deductibles and relies on federal subsidies to help lower-income families purchase coverage. Insurance companies would have to take all comers, and people could shop for insurance within new state marketplaces called exchanges.

Medicaid would be expanded, and though employers wouldn't be required to cover their workers, they'd have to pay a penalty for each employee who sought insurance with government subsidies. The bill is paid for by cuts to Medicare providers and new taxes on insurance companies and others.

Last-minute changes made subsidies more generous and softened the penalties for those who don't comply with a proposed new mandate for everyone to buy insurance. The latter change drew the ire of the health insurance industry, which said that without a strong and enforceable requirement not enough people would get insured, and premiums would jump for everyone else.

The Associated Press contributed to this report.