WASHINGTON — After years of Republican-led debate over how to pare back Social Security’s rising costs, Democrats are flipping the script with an ambitious plan to expand the New Deal-era social insurance program while making gradual changes to keep it solvent for the rest of the century.

The Social Security 2100 Act, which was introduced this past week in the House and the Senate, represents a sea change after decades dominated by concern that aging baby boomers would bankrupt the government as they begin drawing benefits from Social Security and other entitlement programs. It would be the first major expansion of Social Security since 1972 and the most significant change in the program since 1983, when Congress stepped in to avert a financial crisis by raising taxes and the eligibility age for Social Security.

The bill would provide an across-the-board benefit increase equivalent to about 2 percent of the average Social Security benefit. It would raise the annual cost-of-living adjustment to reflect the fact that older Americans tend to use more of some services like health care. And it would increase the minimum benefit to ensure that workers with many years of low earnings do not retire into poverty.

The bill would cut federal income taxes on Social Security benefits for about 12 million middle-income people while raising taxes elsewhere. The payroll tax rate would rise to 14.8 percent over the next 24 years, from 12.4 percent, and the payroll tax would be imposed on earnings over $400,000 a year.