WASHINGTON  After months of relentless courting and suspense, Senator Olympia J. Snowe, Republican of Maine, cast her vote with Democrats on Tuesday as the Senate Finance Committee approved legislation to remake the health care system and provide coverage to millions of the uninsured.

With Ms. Snowe’s support, the committee backed the $829 billion measure on a vote of 14 to 9, with all the other Republicans opposed.

“Is this bill all that I would want?” Ms. Snowe said. “Far from it. Is it all that it can be? No. But when history calls, history calls. And I happen to think that the consequences of inaction dictate the urgency of Congress to take every opportunity to demonstrate its capacity to solve the monumental issues of our time.”

Ms. Snowe’s remarks silenced the packed committee room, riveted colleagues and thrilled the White House. President Obama had sought her vote, hoping that she would break with Republican leaders and provide at least a veneer of bipartisanship to the bill, which he has declared his top domestic priority.