According to the U.S. Energy Information Administration a 25 day supply of gasoline on hand. What is also relevant is that we are using 88% of our overall refinery capacity.
So it does not take much to throw the system out of tune. When 2 refineries were shut down at the approach of Hurricane Ike much of the Southeast experienced a severe gas shortage. Gas satiations only stock for normal usage, and resupply trucks generally only deliver ½ of the stations capacity at a time. So a shortage combined with panic purchases quickly causes shortages and long lines. The continued topping off makes the shortage last even longer.
In the North Carolina Energy Emergency Plan, there is only one proactive measure (versus usage reduction) noted. State Petroleum Fuel Set-Aside (p46):
Assist petroleum product suppliers in providing product to designated priority end-users in circumvention of federal non-discriminatory marketing rules and assure that priority end-users have fuel available for vital public services.
As they go into details, they show that they are willing to get pretty heavy handed. One open question is how cooperative the private companies will be. In a wide scale disruption, any one State is going to be one amidst many clamoring for supplies.