Sen. Mark Begich (D-Alaska) at a Washington Post Live event. (Drea Cunningham -- The Washington Post)

Social Security is not in danger of becoming insolvent any time soon. According to the program's actuaries, without any changes, Social Security will be able to pay out full benefits until 2033. And there's reason to doubt that problems will arise even 21 years from now. As Jared Bernstein noted when the latest projections came out, the expected date when the Social Security trust fund will be exhausted has varied wildly over the past few decades.

Yet despite its medium-run sustainability, many deficit reduction plans target the program for cuts. For example, Bowles-Simpson introduces means-testing and raises payroll taxes for high earners, but also cuts benefits across the board by adopting a less generous inflation measure, known as "chained CPI," and raises both the minimum age where retirees can claim benefits and the age when they can claim full benefits.

As Nobel laureate Peter Diamond has explained, the latter change is hugely regressive, primarily targeting poor workers in physically demanding occupations. Domenici-Rivlin includes the inflation measure cut, means-testing and payroll tax increase, but leaves out the regressive retirement age increase.

But if one wants to make the program solvent indefinitely without endangering vulnerable seniors, there are options. A new bill from Sen. Mark Begich (D-Alaska), the Protecting and Preserving Social Security Act, provides one method.

The Begich bill would lift the current payroll tax cap, which exempts wages in excess of a certain amount ($110,100 this year) from the tax. In turn, it would give high earners, who would pay more, additional benefits upon retirement, just as benefits increase as wages do for workers below the cap.

According to the Congressional Research Service, a change like that would almost entirely wipe out the program's long-run actuarial imbalance. Specifically, it would eliminate 95 percent of the shortfall, meaning that a mild increase in the payroll tax rate from 12.4 percent to 12.5 percent would be enough to cover the tiny remaining gap. And without any changes at all, the program would be able to pay out full benefits until after 2085. Indeed, the exhaustion date for the trust fund following such a change is so far in the future that CRS didn't even calculate it.

But Begich's bill doesn't just increase taxes for high earners. It also increases benefits across-the-board. While Bowles-Simpson and Domenici-Rivlin adopt a stingier "chained CPI" measure for inflation, Begich adopts "CPI-E," or a measure that specifically captures inflation in goods that seniors buy.

Due to deteriorated health and other considerations, goods seniors buy tend to be more expensive than those younger people purchase. Begich's CPI-E change would mean, effectively, a 4.5 percent benefit increase for the program's beneficiaries, including not just seniors but their designated survivors and disabled Americans as well.

The bill likely will face a steep legislative hill. It amounts to a large tax increase for the rich, including people making between $110,100 and $250,000, and as such would violate Obama's pledge to not raise taxes on people making under a quarter million dollars a year. But given that it makes the tax code more progressive and increases benefits at the same time that it sorts out the program's finances indefinitely, don't be surprised if progressives latch onto it going forward.