I really like this Youtube video on how to do an invisible all-machine binding:
http://www.youtube.com/watch?v=wprg5vzkuGw
How wide you need to cut the binding strips depends on how wide a binding you like and how thick your batting is. A narrow 1/4-inch binding is fairly standard. Assuming an average batting thickness (less than 1/4-inch), then you would probably want to cut your strips 2-1/2".
Here's how it works out. You press the binding in half, so now it is 1-1/4" wide. Then you have to seam the binding to the front or back. That takes up 1/2" (1/4" seams, but two thicknesses). You have 3/4" of binding left to wrap around the edge. 1/4" of that is for the front side, 1/4" of that is for the back side, and the remainder is for the width of the batting.
Oh, and I just saw your problem with not having quite enough binding to wrap around. Just trim the quilt edge until your binding wraps correctly. Next time you might want to cut your binding a bit wider.