I think it's more likely that Cashman gets fired if the Yankees miss the playoffs than he resigns to run for Governor of Connecticut.
As for running for elected office, Connecticut is part of Red Sox Nation. Cashman wouldn't win there, no matter party he affiliated with.
He'd be better off carpetbagging across the New York State line and trying to run against Cuomo.
I think he stays on--if he is fired, he gets demoted to adviser to Steinbrenner---the Steinbrenner family and Cashman go way back---they are like family. Cashman's father, John, helped him get a job in the Yankees organization and he worked his way up in the Yankees organization.....