The Senate voted 60-39 along party lines to set a timetable for likely passage of the bill early Thursday morning.
Democrats also turned back last-ditch motions from Republicans claiming various provisions in the bill, including a mandate that individuals purchase coverage, are unconstitutional.
"It's long past time we declare health care a right and not a privilege," Senate Majority Leader Harry Reid, a Nevada Democrat, said after the vote.
"Today is a victory ... for American families," proclaimed Sen. Max Baucus, D-Montana. "Americans won."
The expected victory for President Obama's top domestic priority comes after nearly a year of sharply polarized deliberations on Capitol Hill. Any measure passed by the Senate, however, will still have to be merged with a $1 trillion plan approved by the House of Representatives in November.