Even if I finally found Web workers:error and debugging article that explains it well and exensively, I just had to report that developing with Firefox is still the right choice in most case.
What happen in Chromium if you try to importScripts() jQuery? Simple: no error message. The problem is that jquery refer to window object that does not exist in worker environment, but onerror event is not implemented, you neither will know there is a problem if you are using Chromium browser.
Javascript Web Workers: From Basics to jQuery.Hive series in part 3 explains how to use a reduced version of jQuery, however now Internet Explorer support web workers, so it is time to use it.