The Senate should pay attention to the health care reform bill unveiled on Thursday by House Democratic leaders. The bill would greatly expand coverage of the uninsured while reducing budget deficits over the next decade and probably beyond. It includes a public option that is weaker than we would like, but it still deserves to be approved by the House.

The coverage expansions would carry a net cost to the federal government of $894 billion over the next decade, according to the Congressional Budget Office. Yet the bill would generate enough revenue from new taxes and from savings in Medicare to offset that cost and reduce the deficit by $104 billion over the course of the decade.

The chief source of tax revenue would be a surcharge on the portion of annual income above $1 million for couples and $500,000 for individuals. The wealthy prospered enormously from tax cuts under the Bush administration. It is fitting that they pay a heavy share of the cost of health care reform.

The bill requires employers, except for small businesses, to offer health coverage to their workers and pay a substantial share of the premiums or face a big penalty. That would be a useful prod to make insurance more available and affordable to employees.

The bill would meet President Obama’s insistence that health care reform not add to the deficit — provided Congress holds firm on slowing the growth rate of payments to health care providers serving Medicare. Of special importance, the trend line for deficits would be heading down toward the end of the decade, suggesting that it would continue on down thereafter. This is a fiscally prudent bill, not a reckless dash toward ever-higher deficits as Republicans contend.

(To make ends meet, the Democrats dropped a costly fix for the unrealistic formula used to reimburse doctors under Medicare. That will be tackled in separate legislation, and ought to be paid for with new revenue.)

Under this bill, the number of uninsured would plummet. Since Congress is determined to exclude illegal immigrants, the salient fact is that by 2019, the bill would provide insurance to 96 percent of all nonelderly citizens and legal residents, leaving about 12 million of them uninsured. It would achieve this feat by making a lot more people eligible for Medicaid, a program for the poor, and by helping tens of millions of low- and moderate-income people buy policies on new insurance exchanges, in which private plans and possibly a public plan would compete for people who lack employer-provided insurance or work in small companies.

Speaker Nancy Pelosi wanted a strong, money-saving public option that would pay hospitals and doctors based on Medicare rates, but she could not win over enough conservative Democrats. Her fallback is to have the secretary of health and human services negotiate rates with health care providers as private insurers do.

The Congressional Budget Office considers this so weak that it might attract only 6 million of an estimated 30 million people buying insurance on the exchanges in 2019. Its premiums might exceed the average private plan, in part because the sickest people might migrate to the public plan.

Still, the House bill has a lot of provisions for consumers to like. It would require insurers to allow young people through age 26 to remain on their parents’ policies. It would provide immediate help to people who have been uninsured for several months or denied coverage because of pre-existing conditions. It would speed elimination of a gap in drug coverage for Medicare beneficiaries (the so-called doughnut hole) and would give the government power to negotiate drug prices on behalf of Medicare beneficiaries, a promising way to reduce costs.

The bill would take a long stride toward universal coverage while remaining fiscally responsible. Senate leaders should try to do as well.