Trump's attorneys, for whatever reason, denied the rationale behind the payment.
If some woman tries to extort you over your banging her even tho she signs a statement saying that you didn't, you say that you didn't, and your lawyer doesn't believe the story, what comes to mind ?
1st, hopefully MrsThePAMan.
2nd, your job. Or your business.
3rd, whether or not you may lose the race for city council is really not that important. Or POTUS if you make it that far.

If TSJ gets convicted, guilty or not, there's a pretty good chance that the damage to his character will remain with him forever. Jobs and positions come and go.
Costello will say that the 1st thing that Cohen mentioned was Melania. Apparently the jury isn't supposed to hear those portrayals of the conversations between Costello and Cohen.