I'm glad the days of carburetors is pretty much gone. Done thousands of them, mostly from cars and trucks and a number of bike ones, but the bike ones always gave me the most problem. Getting the carb off a mid 90's Evolution can be a bit challenging depending on the carb type. Probably is the needle and seat but like others said, the float needs replaced also. Sometimes the carb will overflow on the stand, but upright it will work OK.

 

I'm not familiar with Harley carbs but if it's easy to get to the bowl, you can do no harm taking the bowl off, dump the bowl then clean it, verify the float moves up and down, let a little fuel through the petcock for a second and put the bowl back on. The worst you can do is have the same problem but on the bright side, it may work right when your done. Costs nothing but a few ounces of wasted fuel to try it and you really can't hurt anything or make it worse. If it's been sitting over the winter with gas in the bowl, it may just be gummed up and need a little cleaning.

I can understand being nervous over a complete carb rebuild, but taking the bowl off and having a look at the float is very simple.

Good luck!

 

When this happened to me, I just loosened the 4 screws petcock closed. And between the gas still in the bowl and in the hose it flushed itself.
Never had another problem. But I also never leave the petcock open anymore and walk away.