[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2009/images/12/04/art.getty.capitol.dome.jpg caption="Democrats find compromise on public option elusive."]
Washington (CNN) - As senators prepared for a rare weekend session to continue debate on health care, evidence of the Democratic leadership's biggest challenge was on display: two senators whose votes are key to passing a bill said they have yet to see a compromise they can support on the most contentious issue - the public option.
"There are a lot of discussions going on and I'm going to work hard to see if there isn't somewhere to be in terms of a compromise, but I haven't seen it yet," said Sen. Blanche Lincoln, D-Arkansas, who made a rare appearance before the cameras to push an amendment on another issue.
"I have been very clear, I don't support a public option that is government run or government funded, that puts the taxpayers at risk in the long run," added Lincoln, who is facing a tough re-election battle next year.
In a separate appearance, Sen. Joe Lieberman, I-Connecticut, was less open to compromise, saying he won't be satisfied until the public option is stripped entirely from the health care bill.
"I think the better political compromise is to get the public option out of there and do the rest that's good," said Lieberman, a former Democrat who is still counted as a member of the Senate Democratic Caucus. Lieberman, like Lincoln, supports much of the Democrats' enormous health care bill.
Lincoln and Lieberman, along with Sen. Mary Landrieu, D-Louisiana, and Sen. Ben Nelson, D-Nebraska, all oppose a public option, but they are four votes Democratic leaders would likely need to reach the 60 vote threshold to pass a health care bill.
Although Democratic leadership sources think they could afford to lose one of these Democrats, if they are able to secure the support of Sen. Olympia Snowe, R-Maine, who has also been open to compromise.
While the Senate has been debating and voting on amendments, Senate Majority Leader Harry Reid, D-Nevada, has been working behind the scenes with key senators and White House officials brainstorming and negotiating on a public option.
Sen. Tom Carper, D-Delaware, has been floating one idea for a government run health care option to be offered state by state. States would offer a public option only if they do not have other affordable coverage through existing plans.
But Lieberman rejected that idea. Lincoln would only say that she is "looking at everything."
"I'm going to judge it based on whether there are long term risks to the taxpayers and whether it's government funded and government run," said Lincoln.
Complicating work towards compromise with conservative Democrats is the fact that several liberal Democrats are reluctant to vote for a health care bill that doesn't have a public option. Many consider what's in the bill – a government run insurance option allowing states to opt out – compromise enough.
Much of the work towards finding that delicate middle ground has been going on behind closed doors of the Democratic leader's office.
Democratic leadership sources say Reid is hoping to a find compromise proposal by sometime next week, and part of the reason that he is holding a weekend Senate session is to keep senators in town, and keep negotiations going.
These Senators don't need to vote for the bill, they just need to vote for cloture so the rest of the Senators can vote. If the public option is funded by premiums, I don't see what their objection is really.