In situations where the divide between the two parties is close, internal divisions could make achieving that goal difficult, forcing consideration of a more consensus candidate. No matter which party wins control of the House in November, the split between the two is expected to be narrow for the new Congress convening in January.

Given that expected divide, members of the Problem Solvers Caucus believe they can use their leverage to win adoption of some of the proposals in the rules package written for the next Congress. They say they intend to try to enlist lawmakers outside their group to support the plan and note that many members of both parties believe they are being shut out of House decision-making.

Many of the proposals are aimed at ensuring that legislation with broad bipartisan backing gets an airing in committees and on the floor. Under the proposal, any bill that gains at least 290 co-sponsors or a majority of support from each party would have to receive committee review and be sent for floor consideration in 30 days.

Members of both parties have complained that Republican leaders, fearing political fallout and attacks from the right, refused to take up legislation that would easily pass with the combined support of Republicans and Democrats. (Changes in immigration law are a notable example.) But House Republicans have, for the most part, operated under an informal standard that says that only bills that can attract a majority of Republican support should be considered, severely constraining the agenda.

“We’ve seen time and again how our common sense solutions get jammed up in a system built to empower the voices of a few extremists,” said Representative Josh Gottheimer, Democrat of New Jersey and a chairman of the group.

The proposal is certain to meet resistance from leaders of both parties who do not want to see their power diluted. Considerable authority has been concentrated in the House leadership suites in recent decades, and senior lawmakers want to remain in control of both the floor and the committees.

But members of the Problem Solvers Caucus say the low public standing of Congress is evidence that significant changes need to be made. They say the current moment is the time to push the proposal because it is uncertain which party will control the House next year.