Ideally, the Yankees miss the playoffs, decide they have to have Pujols, and are forced to dump Teixeira for much less than he's worth when he refuses DH so they can move his salary. Then the Cubs pick Tex up for 5 years/$23M per year (plus a couple of mid-level prospects) instead of Pujols for 8-10 years/$30M per year.
If you think contracts like Ramirez's, Fukudome's, and Zambrano's are bad, just wait to see what happens with Pujols' contract by year 6 (maybe earlier if he turns out to be a little older than his listed age). The Cubs shouldn't go beyond 5 years on him.