Browser support for parsing strings is inconsistent. Because there is no specification on which formats should be supported, what works in some browsers will not work in other browsers.
Try Moment.js - it provides cross-browser functionality for parsing dates:
var timestamp = moment("2013-02-08 09:30:26.123");
console.log(timestamp.milliseconds()); // return timestamp in milliseconds
console.log(timestamp.second()); // return timestamp in seconds