Becker doesn't have many cards to play, but one he does have is resignation.
Despite the charges, he's still the mayor and there's really nothing compelling him to leave office - it certainly can't get any worse. Resigning would be what's best for the city, but when you're looking at a lengthy prison sentence on child sex charges it's safe to say personal interest comes first.
It's unlikely Becker wants to drag this out. He's not going to win at trial, and it's almost certain he's going to prison. Now, it's about negotiating how long that prison sentence will be. His best bet may be to trade a resignation for pleading guilty to reduced charges. That would allow the city to move forward and probably lessen his prison time.
That said, the City Council could just wait him out, remove him from office and move one without a resignation. But that could get messy, and embarrassing, for Racine.
In talking about this case, a number of people had said something along the lines of: "Racine doesn't need this." They're right. Swinging one last deal with Becker before he heads off to prison may be the best way to make this disappear sooner, rather than later.