They will hold a senate investigation into the matter, which anyone in the right mind should be terrified of. They will start issuing subpoenas to people in charge at Yahoo, and start asking them questions on national t.v., (which will likely be embarrassing and detrimental to Yahoo's stock price and reputation). Provided that nobody tries to cover anything up (Federal prison time for lying under oath to a senate investigation), the company might get off with a reprimand, provided that there aren't any laws that were discovered to have been broken. But Senators aren't going to sign up for this investigation to NOT prosecute people for covering this up, so they will be out for blood. There is a good chance that something will have been done wrong, and some larges fines will be implemented.
I predict that there will be a number of c-level and VP early 'retirements', when yahoo's board of directors boots people for putting them in the spotlight like that. Following the investigation, expect a few new federal hacking disclosure laws to hit the books next year. This will probably not go well for Yahoo, short their stock now.