Why Republicans are not going to get traction comparing Christie to Obama.
With political scandals the details are specific to each politician and situation.
Trying to compare a governor to a president is particularly unwise. Their roles are much too different and staffing arrangements and organization are much different. New Jersey is a populous state so it has a large government but it isn't the United States.
What makes any scandal "have legs" is
(1) if a direct connection to an elected official is established or strongly suspected.
(2) if it appears that there was a cover-up or attempted cover-up.
(3) if the elected official is on tape making dismissive remarks using sarcastic humor about the scandal as it is still unfolding and later these remarks are shown to be way off target.
(4) If there is a strong sense in the public that specific actions were illegal or should be illegal.
(5) if it plays into an accepted perception about an elected official or administration.
(6) if the large parts of the public can easily identify with specifics of the actual scandal.
Any one of these is a big problem for an elected official. Unfortunately for Christie all six of them appear to apply.