Still, he conceded that prospects for the bill in the Republican-controlled Senate were dimmer.

Averting a Pension Meltdown

Lawmakers are to continue efforts to head off an insolvency crisis that could lead to sharp cuts in pension benefits for over a million workers and retirees and drain a federally sponsored insurance backup program.

About 1,400 multiemployer plans cover 10.6 million workers and retirees, according to the Pension Benefit Guaranty Corporation , the federally sponsored insurance backstop for defunct plans. Multiemployer plans are created under collective bargaining agreements and jointly funded by groups of employers in industries like construction, trucking, mining and food retailing.

Plans covering 1.3 million workers and retirees are badly underfunded. And the P.B.G.C. projects that its multiemployer insurance program will run out of money by the end of the 2025 fiscal year, absent reforms .

An earlier bill — the Multiemployer Pension Reform Act passed in 2014 — has faced strong resistance from retiree organizations, consumer groups and some labor unions because it permitted troubled plans to seek government permission to make deep benefit cuts if they could show that the reductions would prolong the life of the plan.

The benefit cut provision of the earlier plan would be repealed under legislation passed by the House in July.

The new bill — the Rehabilitation for Multiemployer Pensions Act — would instead provide low-interest loans to struggling plans, but it faces opposition in the Senate, which is working on its own version. Issues to be worked out include interest rates that plans can use to project future return on investment, any possible increases in premiums paid by pension plan sponsors to the P.B.G.C. and whether any benefit cuts to pension recipients should be allowed.

“With the election coming up in 2020, it’s doubtful that legislation will be introduced in the Senate before then,” said Gene Kalwarski , the C.E.O. of Cheiron Inc. , a pension and health care actuarial consulting firm that is advising multiemploye r plans, advocacy groups and lawmakers on ways to solve the problem. But, he added, “solutions become more expensive by several billion dollars for every additional year that we wait .”