As I said, once you get the TN, it is valid and remains so until it expires or you lose your job. Since presumably neither of these will happen, your
TN will remain valid in the scenario you describe.
I agree with your goal of securing the TN before giving notice, trouble is, many POE will
not grant a TN 'early' (they used to). Some will ask "are you on your way to work now?" if you answer, "no it's in 3 weeks", they may say "come back then" or "come back in a week or two".
One thing you can ask is for them to "preview" your paperwork (again. some will, some won't). If they say it looks fine, then you have some comfort level with getting the TN later. Not a guarantee but I'd go with that.
Another thing you can do is arrange a telecon with your new employer to be done in US right after crossing, to discuss your job etc. So, when asked, you can truthfully say "yes, I have a meeting scheduled for later today".
And, as a last resort, remember that, as the employee, you are not required to give any notice to your employer when quitting. They need to give you notice, not the other way 'round. It is cutomary, and certainly advisable as a good faith measure, but never required.
-- Thu Sep 24, 2009 10:29 am --
Oh, and another reason getting TN 'early' is advantageous: You need the TN (I-94) to give to your mover for his paperwork to ship your belongings into US.