Just a quick note to anyone else who finds this discussion whilst looking for a definitive, or at least authoritative, answer on this topic.

I've just referenced the Associated Press Stylebook 2009 edition and it recommends the following, as a number of posters have already stated:

Two weeks' notice.

Had the notice period been one week, it should have been:

One week's notice.

Whilst I appreciate that the AP are not the arbiters of correct punctuation, it's authority should be sufficient to win any on-going office arguments on the subject.

For your reference the ISBN of the edition I am using is 978-0-465-01262-6