Terrible headline. Makes it sound like Biden is chickening out of something in New Hampshire when the reality is that a Republican campaign to cast him as unable to win the state failed. So he's "set to avoid" it, because the smear campaign failed.
Hmm I don't really see that reading of the headline - avoiding humiliation implies he chickened out? I think it's just saying he's going to... avoid being humiliated, not necessarily through any cowardly means. And the article backs that interpretation up.