Correction: An earlier version of this story incorrectly stated that the U.S. Postal Service earned an operating profit this year. It also mischaracterized a Senate bill proposal for door-to-door delivery. It has been corrected.

Two top senators have introduced a bipartisan bill that would overhaul the ailing U.S. Postal Service, a contrast to House Democrats and Republicans, who remained divided last week as Congress headed into its five-week recess.

Proposed by Sens. Tom Carper (D-Del.) and Tom Coburn (R-Okla.), the legislation would restructure the agency’s prefunding requirement for retirement benefits and allow a gradual end to Saturday mail delivery if deemed financially necessary. The bill would make curbside delivery or cluster boxes mandatory for businesses and new homes, with some exceptions.

“The time to act is now,” Carper said, noting that Postal Service is near financial collapse. “It is my hope that Congress and the Obama administration can come together to enhance this plan in order to save the Postal Service before it’s too late.”

Coburn called the measure “a rough draft of an agreement subject to change that I hope will move us closer to a solution.”

House lawmakers seemed far from a solution last week, however, as Oversight Committee Chairman Darrell Issa (R-Calif.) and Democrats battled over his postal bill. Issa’s legislation was voted out of committee without Democratic support.

Rep. Elijah E. Cummings (Md.), the panel’s ranking Democrat, said in a statement that the measure would “weaken the Postal Service and negatively impact service to all Americans.”

Issa’s proposal also calls for revising the prefunding requirement but requires Saturday delivery to be phased out. In addition, it calls for replacing door-to-door mail delivery with neighborhood cluster boxes. The Senate bill does not insist on these changes.

House Democrats have opposed the potential service cuts.

On Tuesday, Cummings said of the Senate bill: “I’m pleased that Sens. Carper and Coburn recognize the urgency of comprehensive postal reform. While I am still reviewing the proposal, I have serious reservations about some of the provisions in the bill.”

Issa said Tuesday, “I hope that Oversight Committee Democrats will change course and drop their partisan opposition to these bipartisan provisions.”

Labor groups have rejected both measures.

“The legislation on both sides of the Hill is likely to lead to a death spiral for the Postal Service,” said Jim Sauber, chief of staff to the president of the National Association of Letter Carriers.

Postmaster General Patrick Donahoe moved this year to eliminate Saturday delivery without congressional approval, but he withdrew that plan in April under pressure from lawmakers and labor groups. The Government Accountability Office issued a legal opinion in March that said a 2012 congressional requirement for six-day delivery was still in effect, contradicting the agency’s argument that the statute may no longer be binding.

Beyond delivery issues, the Senate bill would revise a 2006 congressional mandate that requires the Postal Service to prefund retiree benefits, allowing for a less-aggressive payment plan. Issa’s legislation would adjust the payment formula as well.

Postal-worker unions have called for a full repeal of the controversial prefunding obligation, saying it has crippled the Postal Service. They also have argued that the requirement is unfair, because Congress has not applied it to any other federal agencies.

Donahoe has also said the Postal Service would do better without the mandate, saying in May that terminating it would be the “single biggest change that would have the least negative impact” among possible reforms.

The presidents of four unions sent a letter to Senate Majority Leader Harry M. Reid (D-Nev.) on Monday expressing “utter dismay” with the Senate bill, saying it would downsize the service to pay for the prefunding requirement, among other complaints.

Another proposal circulating in both chambers addresses most of the unions’ concerns, protecting Saturday delivery and ending the prefunding mandate. A bill by Rep. Peter A. DeFazio (D-Ore.) has seven GOP co-sponsors. Matching legislation from Sen. Bernard Sanders (I-Vt.) has no Republican backing.

The Postal Service has struggled financially in recent years for many reasons, including the roughly $5.5 billion-per-year prefunding requirement and a decline in mail volume. The agency posted a nearly $16 billion loss for fiscal 2012 before falling behind by an additional $3.2 billion during the first half of fiscal 2013.

“Although the situation is dire, it isn’t hopeless,” Carper said. “With the right tools and quick action from Congress, the Postal Service can reform, right-size and modernize.”

Labor groups assert that the agency’s financial situation is turning around and that it would be on track to make an operating profit this year if not for the prefunding obligation.