Yes remove the float and needle and check that the passage through the inlet fitting (from the gas tank) to the needle seat is clear. It sounds like it runs until the bowl becomes empty then starves for gas. If the jet were clogged it wouldn't run at all.
I dug out that nasty little brass tube above the seat and it runs great. The miniature holes on the side get plugged up. Here's a fantastic cleaning guide I referenced today in another Honda post. If you've got anything with the small Honda motor on it recommend bookmarking this like I did