Fortunately, you discovered this on the ground
Jarvis:
Scott is right. Nothing is worth taking risk in an airplane especially when it deals with such a volatile substance as fuel. It could be a stuck float, but the source of the problem could be further upstream.
A leaky float is not going to mysteriously heal itself after you tap on the carb. Once the float is filled with fluid, the carb will flood no matter how hard you bang on it. Or, the float is hanging up on the sides of the bowl because the float is distorted.
Some dirt that got past a ripped/deteriorated membrane in the gascolator and the carb filter could be keeping the needle valve off its seat allowing gas to pour thru.
My guess would be the float but I would not stop there.
If trash caused the needle to remain off its seat, where did the trash come from? Fuel lines (especially flex lines) deteriorate over time and deposit trash further downstream. If the inline gas filter that sits in the carb was improperly installed, it may not be working, or some of the fine wires that comprise that filter could have broken off causing the needle to NOT return into its seat.
So not only must you take the carb apart, but also all of the systems that feed into the carb. There are some special tools required for carb work so don't just clean it and call it a day.
One of the better places to get carb parts is
http://avstardirect.com. I'm sure there are other good vendors, but these folks seemed compenent during the last carb repair we did.
Finally, consider yourself lucky that this problem expressed itself on the ground.