I have discovered the cause of this problem. It was a conflict between a recent Microsoft security update, software for an HP 3970 scanner attached to this computer, and Word 2003.
The following actions solved the problem. First I removed the HP Software for the 3970 scanner. I then checked Word 2003 and found that no longer was hanging on the "save as" command. But that left me without a driver for the scanner, because there was no native XP driver available for it.
So, I then went to the HP website downloaded the latest version of the software for the scanner. I installed the software, then checked Word 2003 and found that "save as" was still working normally.
The key to the solution was a very obscure and cryptic posting on a Microsoft site.