Smoking induces the activity of a liver enzyme called CYP1A2. It seems mostly to be due to certain carcinogens (polycyclic aromatic hydrocarbons) in
tobacco smoke, but possibly also nicotine.
CYP1A2 metabolizes caffeine.
So, more smoking --> speeds up metabolism of caffeine --> you feel coffee less strongly (blood levels go down more quickly)
Smoking cessation --> metabolism of caffeine returns to normal (slows down from what it used to be) --> you feel coffee more strongly.
I've heard more than a few anecdotes from people who have to cut their caffeine intake after quitting smoking.
(Other drugs that are metabolized by 1A2 usually have to be adjusted too.)
There are individual variations in liver enzyme activity, so it's going to be more noticeable to some people than to others.
If your nic intake is the same as it was before or greater, you may or may not notice this effect (it's possible that nicotine has some effect in and of itself on CYP1A2 metabolism).
There may be other mechanisms at work but this is one major and well-studied phenomenon.
The sciencey stuff behind this:
Then
this study in rats also shows an induction of CYP1A2 by nicotine alone. It's a bit controversial still whether nicotine has a particularly huge effect in itself.
You can also see tables of CYP1A2 activity in the Wack-e-peed-e-huh
page.
tobacco is listed as a "potent" inducer.