While lawmakers continue to fight over how to fix the ailing U.S. Postal Service, the agency's money problems are only growing worse.

The Postal Service repeated on Wednesday that without congressional action, it will default—a first in its long history, a spokesman said—on a legally required annual $5.5 billion payment, due Aug. 1, into a health-benefits fund for future retirees. Action in Congress isn't likely, as the House prepares to leave for its August recess.

The...