If that's all you're looking for, almost any "trouble ticket" software would suffice. Something like Redmine (Ruby) or Trac (Perl) or even PHPSupportTickets (PHP). They don't have a specific purpose, other than a ticket software.
In your case, a ticket would be a work request. You can assign each a priority, a specific user to do the work, timers to see how long the work took, percent complete, track history of comments, attach files, etc., etc.
If what you describe above is all you need, then the items I mentioned above (in order of preference) will work. Each ticket can be assigned to a user, each ticket can have a priority, and each ticket can have a due date. All of them can be visible in a grid view. You can even get graphs of how work has progressed and such.
Take a look at the three I mentioned. They are some pretty-good products. I really recommend Redmine. We use it at work and it gets hit hard. Haven't had a problem with it yet. I used to use Trac, but it doesn't support multiple projects (or didn't when I last used it). Neither are PHP-based solutions, but would seem to suffice.