WASHINGTON  Democratic leaders in the Senate on Wednesday unveiled their proposal for overhauling the health care system, outlining legislation that they said would cover most of the uninsured while reducing the federal budget deficit.

Senator Harry Reid of Nevada, the majority leader, said at an evening news conference that the legislation, embodying President Obama’s signature domestic initiative, would impose new regulations on insurers, extend coverage to 31 million people who currently do not have any and add new benefits to Medicare.

Mr. Reid said the bill, despite a price tag of $848 billion over 10 years, would reduce projected budget deficits by $130 billion over a decade because the costs would be more than offset by new taxes and fees and by reductions in the growth of Medicare.

Democrats expressed confidence that they would have the votes needed to move forward when the legislation hits its first test in the Senate, probably later this week. To get past that first procedural hurdle, Mr. Reid will need the votes of all 58 Democratic senators and the two independents aligned with them.