There are a few things certain, namely life, death and Yankees fans calling for the jobs of the Manager and General Manager when the team falls short of expectations. The calendar has barely turned to May and fans and the media have invoked the all too familiar phrase "If George were still alive..."
The Yankees have struggled tremendously out of the gate stumbling to an 8-15 record at the time this was writing. There is still some hope for the Yankees as no team in the AL East has run away with the division however if the ship doesn't right itself, and the Yankees finish with a sub .500 record / last place it is hard to see Joe Girardi, his staff, and Brian Cashman retain their jobs.
Joe Girardi's Staff - Girardi's staff has born the brunt of punishment for failing to make the playoffs in the past, Kevin Long after 2014 and Mick Kelleher, Jeff Pentland did not return after their Wild Card Game loss in 2015. Girardi's staff is not looked on as fondly as Torre's staff to fans. With the Yankees already replacing staff the past few years doing so again may be seen as a half-measure.
Joe Girardi - Manager's are fired because teams can't fire the players. Joe Girardi has never had a losing record in his 8+ years at the helm of the Yankees though he has failed to make the playoffs in 3 of those years, 4 depending on your feelings on the Wild Card Game. It can be argued that in 2013 and 2014 Girardi did a tremendous job of getting those teams to a winning record. Fans despise Joe for his strict adherence to his binder. I like Girardi though I do find myself frustrated with his defined roles for relief pitchers. I believe he is one of the better Managers in the game but with his contract only running through 2017, he could be shown the door.
Brian Cashman - Cashman has been GM since the 1998 season and has seen tremendous success. He has also proven himself to be an evolving GM embracing analytics, an increased focus on drafting and development and more. In recent years, he has consistently made excellent trades acquiring the likes of Didi Gregorius, Nathan Eovaldi, and Justin Wilson. Hal Steinbrenner appears to have full faith in Cashman from top to bottom within the organization. If changes are made I could see Cashman surviving them.
When it comes down to it I think the Yankees will end up recovering from this abysmal start to be competitive. Whether they are competitive enough to ensure no one loses their jobs is still to be seen.