The Senate Finance Committee just killed an amendment proposed by Sen. Chuck Schumer to create a new government-run health insurance plan by a vote of 13 to 10. Coupled with the failure of another version of the so-called “public option” introduced by Sen. Jay Rockefeller earlier in the day, this officially means that the Finance Committee’s health care bill will not include a government-run plan favored by liberals.

The defeat of the government plan in the Finance Committee sets the stage for a brawl among Democrats that will help determine whether or not they’re able to pass health care legislation. Other Democratic health care bills, including the ones from three House committees as well as the Senate Health, Education, Labor and Pensions Committee all include a government plan. Eventually, Democrats will have to find a way to merge all the bills together, which won’t be an easy task.

On the House side, liberal members have insisted that they would not support a bill that did not include what they consider to be a “strong” government plan, meaning tying reimbursement rates to Medicare.

The problem is that when Rockefeller proposed something similar today in committee, five Democratic Senators voted against it. Even when Schumer removed the tie to Medicare rates, three Democrats voted against it: Sens. Max Baucus, Kent Conrad, and Blanche Lincoln. And that’s just the Finance Committee. Other Senate Democrats including Ben Nelson, Mary Landrieu, and Joe Lieberman have publicly opposed a government plan. Taken together, that means at least 8 Democratic Senators oppose what liberals would consider a “strong” government plan, and at least 6 would oppose even a milder version. Schumer himself admitted today that they did not currently have 60 votes to pass the government plan in the Senate.

Thus, the whole health care fight may hinge on whether the White House will be able to get liberal lawmakers to drop their demands for a government plan. This is problematic. The reason is that one of the most obvious ways to win over liberals would be to increase the level of subsidies to individuals seeking to purchase health insurance, yet doing so would substantially drive up the cost of legislation. President Obama has boxed himself into a corner on that front by declaring that his plan would cost $900 billion, and by vowing to veto any bill that adds to the deficit.