1. The Cardinals aren't stupid enough to let him go- He is the face of the franchise. St. Louis is a baseball city. If the Cardinals let Pujols go, there would be a significant backlash from fans and sponsors. Baseball would still be played and the Cards would still be ok, but their would be a hit in attendance.
2. Pujols has said he wants to be a "Cardinal for life"- Not the best move in terms of negotiations by Pujols, but it shows he is different than your average player. He is willing to take slightly less money (mind you he will still want and get a record setting contract) to stay a Cardinal. He wants to get this deal done, he wants to be a Cardinal.
3. Most of the talk in the Media is just B.S.- Contract negations are fun to watch because both sides like to pretend no deal is going to happen. In the end, barring stupidity by either party, the deal always gets done. Both sides give a little more than they want, but in the end it all works out. And that what will happen with Pujols and the Cards.
There ya have it, 3 simple reasons the deal will get done and #5 won't be leaving baseball heaven.