Error / warning messages: [function.fopen]: failed to open stream ...

I am getting a lot of error messages in my logs and when I use drush to clear cache. A sample message is:

Warning: fopen(/home/mysite/tmp/filecache-default/cache-ctools_plugin_files:ctools:content_types) [function.fopen]: failed to open stream: Permission denied in DrupalFileCache->set() (line 134 of /home/mysite/public_html/sites/all/modules/filecache/filecache.inc).

There are dozens of these. I made sure the directory is writable on the web server so I am not sure what else might be wrong or what to do. Filecahce is writing files to the directory, I have confirmed that.

Update:
Just a little more info, I set /tmp/filecache-default to 777 and to the user "mysite". However, if I examine individual permissions of cached files within that directory, the permission is set to 644 and user: 99 on each file which I think is Apache. Hopefully that helps.