House Democrats announced a plan yesterday that would force the richest 2 million U.S. taxpayers to shoulder much of the cost of an expansion of the nation’s health-care system, by imposing a surtax of as much as 5.4 percent on income above $350,000 a year.

The House proposal aims to extend insurance coverage to 37 million Americans over the next decade, covering more people through Medicaid and providing subsidies to help others meet a new federal mandate to purchase insurance. Democratic aides said the proposal would cost more than $1.2 trillion over the next 10 years, and would ensure that 97 percent of Americans were enrolled in a health plan by 2015.

About half of the cost would be covered by reducing spending on federal health programs, primarily Medicare, which serves the elderly and the disabled. But much of the rest of the money would come from a new tax on families earning more than $350,000 a year and individuals earning more than $280,000. The taxes, which would take effect in 2011, would affect about 2.1 million taxpayers, the nonprofit Tax Policy Center projected.

The surtax would start at 1 percent and rise to 5.4 percent on income exceeding $1 million. Combined with the expiration next year of tax cuts enacted during the Bush administration, the surtax would drive the top federal tax rate to 45 percent, the highest level since lawmakers rewrote the tax code in 1986.

The House proposes to raise about $37 billion by changing the corporate tax code, but those provisions would be dwarfed by the surtax on the wealthy, which is projected to raise $544 billion over the next decade. Initially, the surtax would add 1 percent to the tax rate on income exceeding $350,000, 1.5 percent on income exceeding $500,000 and 5.4 percent on income exceeding $1 million. But the lower rates could rise again if the cost of health-care expansion exceeded expectations, to 2 percent and 3 percent respectively.