It does work in Firefox (including 2.0.0.20). See http://jsbin.com/akili (add /edit to the url to edit):
<p id="one">One</p>
<a href="#" onclick="document.getElementById('one').id = 'two'; return false">Link2</a>
The first click changes the id to "two", the second click errors because the element with id="one" now can’t be found!
Perhaps you have another element already with id="two" (FYI you can’t have more than one element with the same id).