... I'm not sure if the SS has a spare option or not. Funny you say you'd be embarrassed. I had to do just that when I had my RX8. Called roadside assist... he was like WTF a flat??? I just said "I know I know... No spare" and he laughed and flatbedded my car.
all for a flat tire. I don't have a spare now either... but I do have a nice little air pump.