I'm trying to upload multiple large jpg files, about 3 1/2 meg each.
If I try to upload more than two files I get an upload error saying I must upload at least one file.

I can upload two 3 1/2 meg files at a time with no problem.

I have uploaded multiple jpg files that are small -- say 40kb or so.

This upload error on happens with the big files. I'm no where near the 7mb limit for any one file.

The limit for one file is 2MB, not 7 but you are not near that either. But it may not be the upload that is failing. Perhpas your installaton does not have sufficient memory to process and display the large files.

If you have that many large files to upload, I would recommend uploading via FTP instead of the web uploader.

Also, if you are on a shared server you might think about resizing these images before uploading.

The program clearly says 7MB upload limit.
The following text is copied from the upload screen.
"The maximum size for any one file is 7MB."

I'm not making this up, this is what the program says.

2MB is what the vast majority of people will see there, however the upload limit can vary from server to server. Mine happens to say "The maximum size for any one file is 50MB.". It depends on what "upload_max_filesize" is set to in your php.ini file and 2MB is the default. You may want to check the "post_max_size" and "memory_limit" settings to see if they are set too low.