The Delaware Democrat has been working steadily to push Congress to prevent the default, Roll Call reported Tuesday.
The Postal Service must pay $11 billion to the U.S. Treasury by Sept. 30 to cover employee retirement programs. The first payment of $5.5 billion is due Wednesday.
Postal officials don't seem alarmed, issuing a statement saying: "This action will have no material effect on the operations of the Postal Service."
Congress has yet to solve the problem. A bill was passed by the Senate in April, but the House has yet to bring its version to the floor.
The Postal Service said in May it would scale back its earlier-announced plan to close 3,700 offices, a proposal senators had vehemently opposed.
Carper has issued press releases, made speeches and even used social media to pressure House leaders to act. He calls the chamber's indecision "baffling."
A top GOP aide in the House said Monday the Postal Service's board of governors had found that the Senate bill was inadequate to rescue the Postal Service.
Carper's response? "Give me a break."