WASHINGTON — Senate Democrats on Sunday sparred with each other over how to fix the nation's troubled health care system, the moderates threatening to scuttle legislation if their demands weren't met and more liberal members warning their party leaders not to bend.

The dispute among Democrats foretells of a rowdy floor debate next month on legislation that would extend health care coverage to roughly 31 million Americans. Republicans have already made clear they aren't supporting the bill.

Final passage is in jeopardy, even after the chamber's historic 60-39 vote Saturday night to begin debate.

"I don't want a big-government, Washington-run operation that would undermine the ... private insurance that 200 million Americans now have," said Sen. Ben Nelson, a conservative Nebraska Democrat.

Nelson and three other moderates — Democratic Sens. Mary Landrieu of Louisiana and Blanche Lincoln of Arkansas and Connecticut independent Joe Lieberman — agreed to open debate despite expressing reservations on the measure. Each of them has warned that they might not support the final bill.

One major sticking point is a provision that would allow Americans to buy a federal-run insurance plan if their state allows it. Moderates say they worry the so-called public option will become a huge and costly entitlement program and that other requirements in the bill could cripple businesses.

"I don't want to fix the problems in our health care system in a way that creates more of an economic crisis," said Lieberman.

The sway held by such a small group of senators has annoyed their more liberal colleagues, who could vote against a final bill if it becomes too watered down.

Sen. Sherrod Brown, D-Ohio, said he didn't think rank-and-file Democrats would feel compelled to go that far. At the same time, Brown warned Democratic leaders not to make too many concessions.

"I don't want four Democratic senators dictating to the other 56 of us and to the rest of the country — when the public option has this much support — that (a public option is) not going to be in it," said Brown.

The Senate bill would require most Americans to carry insurance and provide subsidies to those who couldn't afford it. Large companies could incur costs if they did not provide coverage to their work force. The insurance industry would come under significant new regulation under the bill, which would first ease and then ban the practice of denying coverage on the basis of pre-existing medical conditions.

Congressional budget analysts put the legislation's cost at $979 billion over a decade and say it would reduce deficits over the same period while extending coverage to 94 percent of the eligible population.

The House approved its version of the bill earlier this month on a near party-line vote of 220-215.

Sen. Dick Durbin of Illinois, the No. 2 Democrat in the Senate, said the health care bill must be passed by the end of the year so that President Barack Obama and lawmakers can shift their attention to the economy and improving employment rates.

Such a timeline also would enable Obama to claim victory on a major domestic priority when he delivers his State of the Union speech in January.

But with one-third of Senate seats up for election in 2010, politics will factor heavily into the outcome of the debate on health care.

Sen. Michael Bennet, a junior Democrat who will be seeking his first full term next year in Colorado, where many districts lean conservative, said he would support the health care overhaul even if doing so means losing his seat.

"The thing that our working families need more than anything else is to end these double-digit cost increases that they're having every single year with health insurance," Bennet said.

Democratic Sen. Chuck Schumer of New York said he believes there are enough votes to include a public insurance option in the bill as long as states are allowed to opt out. To do so, all 58 Democrats and independent Sens. Lieberman and Bernie Sanders of Vermont would have to support it.

Lieberman and Nelson have said they object to the public option. On Sunday, Nelson said he is open to negotiating the provision; he said he would prefer allowing states to opt into the program, instead of having to remove themselves.

Senate GOP leader Mitch McConnell said the lingering reservations by moderate Democrats indicate that the party's leaders have gone too far. On Saturday, no Republican voted to begin debate on the bill, which they said would cripple industry and drive up costs for the average American.

"I believe there are a number of Democratic senators who do care what the American people think and are not interested in this sort of arrogant approach that everybody sort of shut up and sit down, get out of the way, we know what's best for you," said McConnell.

Brown, Bennet and McConnell appeared on CNN's "State of the Union." Lieberman appeared on NBC's "Meet the Press." Nelson appeared on ABC's "This Week."