As the original poster of this question, I can report that I am still, eight months later, not able to process EFTPS through the QB Desktop program.  There is nothing wrong with the internet password or login information with EFTPS, or the way it is entered in QB.  This problem just suddenly occurred at the beginning of the year, after having worked perfectly up until that time.

I will tell you all that I have tried all of the tips and tricks that the Intuit/QB teams have suggested, none of which is particularly high tech or other than routine maintenance.  None of it has worked.  I had a telephone consult with a tech specialist who recommended running database utilities, verifying, and compressing the data. That was all done, no errors found in the data file, yet the federal tax payments function still comes back with an error.

The next step recommended was to allow a QB tech person to work with the data to the tune of about $800.  No.  Just no.