There's no real shortcut, until the 5th edition (a couple of years ago) there was no standard date string format supported by JavaScript (Date was merely required to correctly parse whatever toString output, without the format actually used by either being specified in the standard), and as of the 5th edition, the format that is explicitly supported for parsing isn't the same as what you've quoted (instead, it's a simplified version of ISO-8601). So you'll have to parse it yourself, using regular expressions and/or brute force (String#indexOf, String#substring, String#split), or use a library (like DateJS) to do it for you.
That said, every browser I tried was happy to parse it for you just via new Date, e.g.:
var str = "Sun Jan 08 2012 00:00:00 GMT+0530 (Sri Lanka Standard Time)";
var dt = new Date(str);
Live example I tried IE6, IE9, Chrome 15, Opera 11, Firefox 9, Firefox 5, Safari 5, Konquerer 4.7.3, and Midori 0.4.0 (spread across Windows and Linux). So if you're happy with that and you test in your target environments (which I don't know are web browsers, JavaScript is used on servers and desktops as well), you may be happy with just doing that.