Make sure that you have set your 5 digit Zip Code in the Configuration ... Shipping/Packaging ...
Postal Code
Enter the Postal Code (ZIP) of the Store to be used in shipping quotes. NOTE: For USA zip codes, only use your 5 digit zip code.
Ensure that you are using the current USPS shipping module for the January 27, 2013 from:
http://www.zen-cart.com/downloads.php?do=file&id=1292

When you go to the Modules ... Shipping ... and click on USPS, what do you see in the right hand panel?

Ensure that you have switched your site to the Production Server as the Test Server does not work correctly ...