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That measure would postpone a move to five-day-a-week mail delivery for at least two years and require additional layers of review before the agency closes postal branches and mail processing centers.

“The solution to the Postal Service’s financial crisis is not easy but must involve tackling more significant expenses that do not drive customers,” Ms. Collins said.

In the event of a shutdown because of bankruptcy, private companies such as FedEx and UPS could handle a small portion of the material the post office moves, but they do not go everywhere. No business has shown interest in delivering letters everywhere in the country for a set rate of 44 cents or 45 cents for a first-class letter.

Ruth Goldway, chair of the Postal Regulatory Commission, said the planned cuts could test the limits of the Postal Service’s legal obligation to serve all Americans, regardless of geography, at uniform price and quality.

“It will have substantial cost savings, but it really does have the potential to change what the Postal Service is and its role in providing fast and efficient delivery of mail,” Ms. Goldway said.