As it seems there is a internal web server feature in WebStorm, but it is not yet(?) available in IntelliJ. We have been busy providing a proof of concept using AngularJS and BlueEyes and this is helping out with quickly running a web server and serving files using 'http://'
It is easy to run a web server using the "external tool" option from the settings (however it does not integrate with the rest of IntelliJ. For example when you choose "Open in Browser", it will open the 'file://' URL for the resource.
Anyway perhaps you didn't think of it (as it is not rocket science :)
The settings below assume Node.js
http-server is installed. First install Node.js and then install http-server using npm:
$ sudo npm install http-server -g
Here is a screenshot which illustrates configuring IntelliJ:
Note, if you don't want to install Node.js, you could also use
"python -m SimpleHTTPServer" as the command (make sure you set the working directory). However Node.js' http-server is much faster.