The six senators working privately on a health care reform compromise will not be "held hostage" by any deadline, a lead Democratic negotiator said Sunday, suggesting that they might not finish by mid-September as expected.

Negotiators on the Senate Finance Committee, the last of five committees to consider reform legislation, have been working toward reaching a bipartisan compromise by Sept. 15. The date had been described as a deadline.

But Sen. Kent Conrad, D-N.D., said Sunday that while negotiators hope to finish by mid-September they will "not be bound" by a deadline if they feel the bill is not ready.

"What we have agreed to is that we are going to be ready when we're ready," Conrad, one of the negotiators, told "FOX News Sunday." "This is not something that should be held hostage to any specific deadline."

President Obama has already seen one of his self-imposed deadlines fly by. He had wanted the full Senate and House to vote on their versions of the legislation before the August recess. Neither chamber took action by that time.

Public opinion has turned increasingly sour on the Democrats' health care plan the longer it stays on the table, so Conrad's suggestion that the Senate might need even more time may not be seen as welcome news by the White House.

But the Senate Finance Committee has also been trying to hammer out a bill that is more palatable to Congress and the public. Conrad said Sunday, for instance, that the so-called public option — a government-run health care plan - does not have the votes to pass the Senate and that he would continue to push for an alternative system of nonprofit insurance cooperatives.

Meanwhile, Obama wrote in an op-ed Sunday that he's "confident" lawmakers can reach a consensus on health care reform and that the legislation must pass this year.

"We have broad agreement in Congress on about 80 percent of what we're trying to do," Obama wrote.