WASHINGTON -- The House of Representatives headed toward a historic vote scheduled for Saturday on a bill overhauling the health-care system, with Democratic leaders acknowledging they haven't locked down the votes needed to pass it.

On Friday afternoon, Democrats estimated they were 10 to 15 votes short of getting to a majority of 218, as lawmakers balked on issues ranging from abortion to costs to immigration. There was a possibility debate would begin Saturday morning with no sure outcome guaranteed.

The...