The U.S. Postal Service could lose up to $10 billion and have little more than a week’s worth of money left in the bank when its fiscal year ends Sept. 30, the nation’s top postmaster will tell Congress Tuesday.

Postal officials are hoping the latest numbers will finally compel lawmakers to grant them new legal authority to alter delivery schedules, close post offices and lay off hundreds of thousands of workers.

Competing legislative proposals from Democrats and Republicans in the House and Senate are pending, and Postmaster General Patrick R. Donahoe wants lawmakers to vote by month’s end, when the Postal Service will have to pay more than $7 billion in statutory labor and health-care costs that Donahoe says are chiefly responsible for its financial collapse.

According to Donahoe, mail volume fell again this year to only 167 billion pieces delivered, down 22 percent from four years ago, partly because Americans are paying bills online and sending electronic invitations instead of paper ones.

“The way people work, interact, learn, communicate, do business, and live their daily lives is vastly different than it was for our parents and even for many of us,” he will tell senators, according to his prepared testimony. “The Postal Service has a place in this new world, but getting there requires us to change and adapt in ways that might not have been thought of before.”

Donahoe’s estimate of a $10 billion annual loss could change, depending on how much interest USPS will owe to the Labor Department as part of its accumulated workers’ compensation liability of more than $12 billion, according to his testimony. The rest of the loss comes from a roughly $1.3 billion payment to the workers compensation fund and about $5.4 billion owed to fund benefits for current and future postal retirees.

Donahoe will testify before the Senate Homeland Security and Governmental Affairs Committee, chaired by Sen. Joseph I. Lieberman (I-Conn.), who said he hopes Congress moves quickly to ensure USPS “remains a relevant part of our 21st century communications infrastructure, rather than an 18th century relic.”

But Congress has rejected requests by USPS to repeal a law requiring six days of mail delivery so that it can stop delivering mail on Saturdays — a move backed by a majority of Americans that could save the Postal Service $3 billion annually.

Beyond that, the Postal Service wants congressional authority to break its agreements with labor unions so it can lay off about 120,000 workers. The Service also hopes to withdraw its 480,000 pensioners and roughly 600,000 workers from the federal employee health-benefits program and create its own.

But John Berry, director of the Office of Personnel Management, plans to tell senators that postal workers are well-served by their existing health and retirement benefits and the issue should be studied closely before any changes are made, according to his prepared testimony.

Testimony from Tuesday’s hearing was provided in advance by congressional sources.

Even as he asks Congress for changes, Donahoe plans to outline a series of cuts that, combined with congressional action, could shrink the Postal Service over the next four years into to an organization employing about 425,000 people at a cost of $60 billion annually — or $20 billion less than today.

Cliff Guffey, president of the American Postal Workers Union, says Donahoe’s plans are counterproductive. “The Postal Service, having been engaged in several years of cost cutting, has become like the man whose only tool is a hammer,” Guffey plans to tell lawmakers. “To him, everything looks like a nail.”

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