WASHINGTON  The White House and Senate Democratic leaders seem willing to give Senator Ben Nelson, Democrat of Nebraska, just about anything he wants to win his support of major health care legislation. Anything, that is, but the item at the top of Mr. Nelson’s wish-list: air-tight restrictions on insurance coverage for abortions.

The bid to win Mr. Nelson’s support has become a race against the clock. The Senate majority leader, Harry Reid of Nevada, has developed plans for a series of votes beginning at 1 a.m. Monday and round-the-clock Senate sessions intended to meet his deadline of completing the health care bill before Christmas.

But Mr. Reid is still at least one vote short of the 60 he needs to move the bill ahead, and as much as anyone, Mr. Nelson appears to hold the legislation’s fate in his hands.

Other Democrats, liberals as well as centrists, have not yet committed to vote for the bill. And the abortion provisions are just one of numerous concerns that Mr. Nelson has expressed about it. But the biggest obstacle seems to be his demand for tighter restrictions, which are being resisted fiercely by a bloc of senators who support abortion rights.