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.

Doug Mills/The New York Times

Senator Harry Reid, the majority leader, was joined by other Democrats as he discussed the Senate’s health care plan at a news conference on Capitol Hill on Wednesday.

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.

That vote would clear the way for what is sure to be an unpredictable roller-coaster ride of a debate on the Senate floor through much of December. Earlier this month the House passed its version of the health care legislation.

Republicans have vowed to fight the legislation at every turn, saying it represents a dangerous expansion in the role of government that would increase taxes and insurance costs for millions of people. “It’s going to be a holy war,” said Senator Orrin G. Hatch, Republican of Utah.

Under Mr. Reid’s bill, the government would establish a new public insurance plan, which would compete with private insurers. States could opt out of the public plan by passing legislation.

In one last touch on Wednesday, Mr. Reid and his aides finally named the bill that he wrote over the last few weeks, selecting parts of bills previously adopted by two Senate committees. It is called the Patient Protection and Affordable Care Act. “This legislation is a tremendous step forward,” Mr. Reid said. “It saves lives, saves money and will make Medicare stronger.”

Though broadly similar to the House bill, Mr. Reid’s proposal differs in important ways. It would, for example, increase the Medicare payroll tax on high-income people and impose a new excise tax on high-cost “Cadillac health plans” offered by employers to their employees.

Mr. Reid’s bill would not go as far as the House bill in limiting access to abortion. And while he would require most Americans to obtain health insurance, he would impose less stringent penalties on people who did not comply.

Many provisions of Mr. Reid’s bill, including the creation of insurance markets, or exchanges, would take effect in 2014, a year later than similar provisions of the House bill. The delay is intended primarily to reduce the cost of the legislation.

Both bills would create a voluntary federal program to provide long-term care insurance and cash benefits to people with severe disabilities.

Desperately seeking money to pay for the legislation, Mr. Reid came up with a new source of financing: a 5 percent tax on elective cosmetic medical procedures. The tax would be paid by patients, but collected by doctors and clinics and forwarded to the government.

The tax would be calculated as 5 percent of the amount paid for an elective cosmetic procedure, whether by the patient, insurance or other sources. The tax would not apply to cosmetic surgery for people with congenital abnormalities, disfiguring diseases or traumatic injuries.

The official cost analysis released by the nonpartisan Congressional Budget Office shortly after 11 p.m. showed that Mr. Reid’s bill came in under the $900 billion goal suggested by Mr. Obama. But 24 million people would still be uninsured in 2019, the budget office said. About one-third of them would be illegal immigrants.

The Congressional Budget Office has said the House bill would reduce deficits by $109 billion over 10 years and cover 36 million people, but still leave 18 million uninsured in 2019.

Republicans and some independent budget analysts said, however, that the savings might not be fully achieved because they were based on unrealistic assumptions about a sustained increase in the productivity of health care providers and much slower growth in Medicare spending.

Rahm Emanuel, the White House chief of staff said Mr. Reid’s bill was impressive. It “meets the president’s objectives, provides protection from insurance companies, contains true cost controls and extends coverage to working families,” Mr. Emanuel said.

Senate Democratic leaders were still trying frantically on Wednesday to nail down a few of the 60 votes needed to begin debate on the legislation.

Vice President Joseph R. Biden Jr. and Interior Secretary Ken Salazar, both former senators, were on Capitol Hill, trying to help Mr. Reid round up votes.

The proposed tax on “Cadillac health plans” is among the most contentious provisions of the bill.

Under the Finance Committee bill, the government would have levied a 40 percent tax on the value of insurance exceeding $8,000 for individual coverage and $21,000 for family coverage, with some exceptions.

Under Mr. Reid’s bill, the tax would kick in at higher thresholds, $8,500 for individuals and $23,000 for families.

Some economists say the tax could slow the growth of health spending by encouraging employers to pare back health benefits. Many labor unions oppose the tax, saying it would hit many middle-income workers who have sacrificed wage increases to secure or retain health benefits.

The proposed increase in the Medicare payroll tax is another major new feature of Mr. Reid’s bill. Under current law, employers and employees each pay a tax equal to 1.45 percent of wages. Mr. Reid would increase the rate to 1.95 percent for individuals with annual incomes over $200,000 and couples over $250,000. The tax on employers would be unchanged.

Senate Democratic aides said the payroll tax increase would raise $54 billion over 10 years.

By contrast, the main source of new revenue in the House bill is a surtax on high-income people. The tax would be 5.4 percent of adjusted gross income exceeding $1 million for couples and $500,000 for individuals.

Mr. Reid’s bill would also raise revenue by levying annual fees on health insurance companies and pharmaceutical manufacturers. The Finance Committee would have imposed fees of $4 billion a year on manufacturers of medical devices, but Mr. Reid decided to cut those fees by half.

Under the bill, most people would be required to carry insurance. A person without insurance could be required to pay a financial penalty, starting at $95 in 2014 and rising to $750 in 2016, with a maximum of $2,250 for a family.

The Senate bill would not explicitly require employers to offer health insurance coverage. But if an employer with more than 50 employees does not offer coverage and if any worker qualifies for a federal subsidy, the employer would have to pay a penalty, typically $750 for each of its employees.