Cotton knew his brief, and the presentation of that brief, much better than Alexis did his. Add in decades of political and rhetorical training and this isn't even a fair fight.
Guys like Cotton can be beaten, but only with 1) a much better case on the facts and 2) a complete mastery of the presentation of that case. This is a long way from home.
EDIT: One of the hardest things in what Alexis is doing is having people criticize how he's doing it. I congratulate him for putting himself out there for his principles and his community. He's up against people who have spent their entire lives training in interested (as opposed to principled) advocacy. He can be a lot better at this, and he can win -- after all, he's right! But he has to get a lot better at the execution.