Isn't that the wrong way around? Instead of pushing to the web server and let it figure out where to put the changes, change the local file (or file on the server, via NFS or such) and push the changes to the browser as well using tools such as swankjs  or, once it's ready, Kite  (that's my pet project).
For higher-level languages like Coffeescript or SASS, run a local compiler on the file or function so you can push the compiled code to the browser.
A nice side effect of this approach is that you can use a real code editor instead of the Notepad-style editor embedded in the browser.
In that regard, my #1 feature request for the Firefox devs is to finish and implement the remote debugging protocol  and, preferably, work with the WebKit devs towards unifying the two protocols.