Are there any tools that can monitor social sites (Facebook, Twitter and so on) usage, and if a particular user has overused his/her daily quota, send him/her a warning?
If its time you want to measure then websense have a web filtering product that may do what you want. It allows you to create custom filtering groups of sites and assign a time-based user quota to them, which may do it for you.
However, websense isn't cheap (though there is a trial version iirc) so this is a lot of money to spend on what is ultimately a bad idea*.
(* they'll only switch to a site you're not monitoring. There are rarely good technical solutions to behavioural problems)
I think this will be harder than you think, and I really don't know how you're going to "count" usage. For example, when at work I normally have the Server Fault main page and chat room open in Firefox. The problem is, just because it's open in Firefox all day making requests (the chat room makes A LOT of Ajax requests polling for new messages) it does not mean I am doing nothing but looking at Server Fault all day. These are just 2 of the many tabs I have open in Firefox, and Firefox is just one of many windows I have open. My point being just because it's open and making HTTP requests, there's a very high chance that I'm not looking at it and actually doing some work.
As far as your request goes, I don't know of any product that does what you want and the best I can come up with is some filtering of your web proxy/firewall logs if either of these provide them. The caveat with this, as I mentioned above is that just because my PC is making obscene numbers of HTTP requests to