WASHINGTON (CNNMoney) -- The Senate on Wednesday passed a plan to save the struggling U.S. Postal Service, an effort that could save thousands of jobs and 100 mail processing plants now slated to be closed or consolidated next month.

In an unusual showing of bipartisanship, the Senate voted 62-37 to throw a lifeline to the indebted Postal Service. Without help, the Postal Service would otherwise cut Saturday service, delay mail delivery and close hundreds of postal processing plants and post offices, triggering thousands of job cuts nationwide.

"My hope is that our friends over in the U.S. House, given our bipartisan steps we took this week, will feel a sense of urgency," said Sen. Tom Carper, a Delaware Democrat, one of the Senate bill's co-sponsors. "The situation is not hopeless, the situation is dire."

The House has yet to take up a different bill to reform the Postal Service. However, Rep. Darrell Issa, a key Republican on postal service legislation, called the Senate bill "wholly unacceptable," in a statement released Wednesday.

Congress faces a deadline of May 15, when a moratorium on postal closures expires.