It's been a few months since you posted, so you may have already solved jamming your problem, but... I just wanted to share my "getting out of a jam" experience (in case anyone else has this problem).
I bought a new button maker (Model 100) from American Button Machines. It arrived yesterday and, in my excitement, I managed to jam it on my third button. Oh no! (I think I put 2 mylars in without realizing it -- total user error, as this machine kicks a**. I love it!)
It came with instructions on how to unjam it which are exactly the same instructions that you pointed to in your post (http://www.buttonsonline.com/tuneup/
-- at the bottom of the page). My boyfriend and I scratched our heads on this for nearly an hour -- the part that they tell you to press down on seems like the *wrong* part (at least, in the wrong way!)
But we finally tried it anyway and voila! It worked!
You get the feeling that you should be "pulling" the parts apart, but what they want you to do is actually push them further together! And, oddly enough, it works. Yay!
If you're still jammed, I hope this helps. For anyone who gets in a jam... just trust the instructions. Okay! Gotta go make some more buttons now!