If your coil is marginal, the lower voltage when cranking can make the difference between starting and not starting. Here is a way to check for this problem. Disconnect the power feed to the coil and hook it up to a battery charger. If it starts quickly under those circumstances then you know what the problem is.
Also, on some the carburetor percolates a little. The technique for that condition is to gently put the gas to the floor, leave it there for about a minute and then without moving it, try starting it again. This requires both feet!