I think your question should actually be: How can I reliably and repeatably update my live servers? What you need is an automatic deployment script. Personally I prefer Fabric, but there are other tools are available.
An automatic deployment script will allow you to run a single command which will go to live servers and update the source code, run any deployment steps (such as minifying javascript) and restart the webserver.
You really don't want to be minifying javascript or css files on the fly, you should do that once at deployment and then have a variable in your code that specifies whether this is a live deployment or not. If the variable is true then your links to the files should be links to the minimized version, if it's false then they should be to the normal versions.
There are a number of programs which perform minimization, one that hasn't been mentioned yet is JSMin.
