WASHINGTON — The U.S. Postal Service, set to run out of operating cash in October, still can’t get Congress to act with any urgency to help solve its problems.

Competing Senate and House proposals to help resolve Postal Service finances expired when the old Congress left Jan. 3, and two senators who’ve pushed for a postal overhaul retired. The post office now must persuade lawmakers focused on broader fights on the deficit and spending to pass a law to let the agency cut costs and plug losses.

“We have a just-in-time Congress that waits until the very last minute before doing things, and I think that will be the likely scenario with regard to postal reform,” Rob Atkinson, president of the Information Technology and Innovation Foundation, said in a telephone interview.

The post office’s fortunes continue to worsen, with the latest estimate pegging losses at $25 million a day. Mail volume is down 26 percent from its 2006 peak. To pay its bills and keep the mail moving, it has had to skip $11.1 billion of required payments over the past two years for future retirees’ health costs. It exhausted its $15 billion borrowing authority last September.

The service says it will run out of money in October even after ignoring this year’s retiree health obligation. If it can’t pay employees or buy fuel for trucks, Americans looking for their bills, magazines and catalogs could find empty mailboxes.

The Postal Service and unions representing its workers have been looking for ways to shore up its finances by getting back surplus contributions to government retirement plans. A Government Accountability Office report last month said those surpluses aren’t as large as previously estimated, making that plan less feasible.

Postmaster General Patrick Donahoe, in a Jan. 3 statement, urged the new Congress to make postal legislation “an urgent priority” as he estimated that the Postal Service is losing $25 million a day.

“We are on an unsustainable financial path,” Donahoe said. “The Postal Service should not have to do business this way.”

About 5 percent of the service’s 525,000 employees last week accepted a cost-cutting early retirement offer. The service says it has already cut about 60,000 full-time jobs in the past two years. If it were a U.S.-based publicly traded company, the post office’s work force would rank as the nation’s second biggest, behind only Wal-Mart Stores.

The service and the National Association of Letter Carriers, whose members deliver mail in cities, announced a new contract on Friday after binding arbitration. The Postal Service failed to win the ability to fire workers without cause. The contract freezes wages for two years, pays new hires less than more senior workers, and lowers employer payments toward employee health insurance premiums.

Donahoe and Deputy Postmaster General Ron Stroman declined, through a spokesman, to comment about the post office’s financial plans beyond Donahoe’s Jan. 3 statement. Stroman, a past staff director of the House committee overseeing postal operations, was hired two years ago to beef up the service’s presence on Capitol Hill.

The Postal Service has a five-year plan for profitability that it revised last year after objections from lawmakers, including opposition to closing rural post offices and mail processing plants that provide jobs and government services in their districts.

It wants to end Saturday mail delivery, close hundreds of letter-sorting facilities and thousands of post offices, and has said it would consider breaking union contracts to fire protected employees. The plan would let it set up an independent health plan, more easily raise rates, and enter new businesses, such as delivering wine and liquor.

The Senate, on a 62-37 vote, passed a measure last April that would have authorized the Postal Service to provide non- postal products and services, revise benefit payment obligations, and offer retirement incentives. The bill, however, would have made it more difficult to quickly close facilities and delayed for at least two years any move to deliver mail five days a week instead of six.

The House didn’t take up that measure. It never scheduled a floor vote on its own postal overhaul bill, which would have created an independent commission to oversee closings, modeled on the Defense Department process for shutting military bases.

Rep. Darrell Issa, R-Calif., who sponsored the House bill, called the Senate measure a “special- interest spending binge” that would keep unneeded facilities open and wouldn’t avert financial collapse.

The House and Senate have to start from scratch with new legislation in the new Congress, which began Jan. 3. Legislation will have to proceed without the Senate measure’s biggest backers, Joe Lieberman, I-Conn., who retired, and Susan Collins, R-Maine, who no longer sits on the relevant committee.

Issa and Sen. Tom Carper, D-Del., who replaced Lieberman as chairman of the Homeland Security and Governmental Affairs Committee, issued a statement Jan. 3 pledging to work together this year to pass postal legislation.

Emily Spain, a spokeswoman for Carper, said the senator “expects postal reform to be a top priority.” Ali Ahmad, a spokesman for Issa’s committee, said nothing has changed since that statement.

Rep. Blake Farenthold, R-Texas, takes over this year as chairman of the subcommittee overseeing the Postal Service.

Atkinson predicted that lawmakers will be forced into a last-minute deal later this year, as the Postal Service comes closer to running out of money and the public hears more about the prospect of an end to mail delivery. Until then, he said the House and Senate probably will reprise their earlier proposals with few changes.

“I would assume when the ‘postal cliff’ gets very close, or they actually go over the cliff, that that would motivate Congress to be able to get over the different positions they have on what should actually happen,” he said.