Some variation on this idea could ultimately appeal to other states grappling with their own exploding pension costs and, in extreme cases, quietly looking for help from Washington. In troubled states, some employees have wondered whether they might be allowed to begin paying in and collecting from the federal system even before they have contributed a career’s worth of taxes.

The potential effect on the Social Security program is hard to estimate. Maine’s proposal would mean new members and a small additional source of payroll tax revenue for the federal system.

Even if it fully embraces the proposal, Maine will have to come up with a considerable sum to sustain its existing pension plan, presumably through some combination of taxes and service cuts. After a phase-in period, Social Security would cover part of state retirees’ benefits, with the state pension as the remainder. Many pension plans in corporate America coordinate their benefits in this way.

The proposal has the advantage of not reducing promised benefits, guaranteed by the constitution in many states. The change would not be cheap, but it would reduce the role of Maine’s pension fund and thus the risk of having to suddenly cover giant losses down the road.

A Social Security spokesman said the agency did not expect many of the holdout states to join, citing the cost of participation. The only other state known to have talked recently about adding Social Security is Louisiana.