So just publicity?
Yes, but ...
I speculate that Williams is hoping, maybe against hope, but might as well try, that Christie or somebody else who is in the news (Trump, some other "dignitary") will say something that helps Williams's cause. Courts follow the wind, in cases like this. If the courts think the politicians want a decision adverse to Cruz, they will deliver a decision that is adverse to Cruz.
That's not to say Courts would follow an opponent's wish - it takes a bigger chunk of the political ball. See Roberts upholding Obamacare, covering a majority of Congress for example. Courts do not want to rock the boat, even when the rest of the government is out of line.