I ran into the same problem and found that the code had changed from 1.5 to 1.6 in the NopSolutions.NopCommerce.Shipping.Methods.USPS.GetShippingOptions method. File is Shipping\Nop.Shipping.USPS\USPSComputationMethod.cs
The code that changed is near the bottom of the method.
In version 1.5 the line is:
if (System.String.IsNullOrEmpty(error) && shippingOptions.Count == 0)
and in version 1.6 the line has changed to:
if (System.String.IsNullOrEmpty(error))
To fix the problem, I changed the code to be like it was in 1.5 and recompiled the USPS project.
Another problem is that if you do get an error back from USPS you only get the generic message of "Shipping options could not be loaded" and not the message from the USPS response. To get a better message in the System Log I added the following code after the ParseResponse method.
if (error.Length > 0)
Audit.LogManager.InsertLog(Audit.LogTypeEnum.ShippingError, error, "USPS Shipping Error");
Then I can see what the real error was in the System Log.
Hope this helps.