if your zoomed out, you can focus on anything right flat up to against the lense. (hopefully it would be against a uv filter though ) the DOF is very thin at that focal distance though... less than a milimenter or so i would guess.
If you are very close to your subject (macro focus range) and determine that you would still like to zoom in some to fill the screen with a small subject, then you could use a achromatic diopter to allow you to do just that.
Distance to lens, with it still being in focus, depends on what your aperture is, your zoom setting, and which camera you're using (the DVX100 or the DVX100A).
The minimum object distance (MOD) that the DVX100 can focus on is approximately 1 meter (3.3 feet). If you zoom into maximum telephoto, and set focus on minimum distance (which is about MF50) then the closest object you can focus on would be about 1 meter away. The more you zoom out, and the more you stop down your iris, the more the depth-of-field will hold, allowing you to move the object closer. And, the more you zoom out, the more of the DVX's macro range becomes available, so you can focus closer. You should be able to get right down to the lens surface in full-wide-angle, but the object won't be very large on the screen.
With the DVX100A, they made a closer MOD -- I think it's .6 meters, or about 1.6 feet.
And, as Terry points out, with the addition of a close-up lens you can effectively move the MOD closer.
Yeah it was funny I remember when the A first came out Steve Golub (the USA DVX100 product manager) loved to show everyone his big Gold ring in focus right against the lens... that was full wide, but it still was pretty impressive.
A diopter is your best bet though, even with the old 100 I can get right up to the lens with a +2.
Based on this thread, I thought I'd give this a try with my 100A. I had objects within a couple of inches in complete focus. Lighting was important (when isn't it?). Another factor was exactly what I was trying to focus on. For example, I tried a page of text, and the black print kept jumping from black to white! I'm sure changing lighting and angles would work around this (but I didn't bother trying).