I have found the root cause of the problem (in my case). I simply eliminate the cause of the problem instead of fixing the plugin, as I'm hoping that the plugin author is reading he can update the plugin to deal with what caused the issue.
View source on your page and make sure there is absolutely nothing after the closing html tag.
This is what was causing my problem (the very end of my html output):
</html><!-- WP Super Cache is installed but broken. The path to wp-cache-phase1.php in wp-content/advanced-cache.php must be fixed! -->
Apparently this the commented after the closing html tag is being appended to the JSON response, causing an error, which in turn causes the spinner to never quit spinning (actually, the element css style for visibility is never updated to "hidden"). In my case, we had moved to another server, and the contents of wp-content/advanced-cache.php (from WP Super Cache) was causing this extra output. I simply uninstalled WP Super Cache, which eliminated the extraneous output to my page.
So check if there's any extra output after your closing html tag. You can also use Firebug to see the XHR response.