dan_fritz:
I know I can active listen to the serial port using Python but how can I then push the data from Python to the clients browser?
You do it by designing your web app so that the browser cooperates with the server to receive updates from the server. This isn't an Arduino question, it's a web app design question, but you have already mentioned AJAX so you already know of one potential solution. There are plenty of other frameworks that support this and you need to pick one (or invent your own, if you don't like using other people's wheels).