Dana,
Thank you for the suggestions. Those sound good. I actually did figure out what my problem was though. That being the case, I will write it here, so that a year or two from now when I have to do this again and I have forgotten what I did, I can look it up. Maybe this will also benefit another clueless Arc user like me.
In the Layout View, I had my map set to the approximate plotter dimensions, 42 x 36. What I actually needed to do was set it to the letter size, 8.5 x 11, by changing the page settings under File. In the Data View, instead of having the whole map visible at a scale of approximately 1:120000, I had to have the scale at something more like what a single page would look like, 1:3000 or something. Then I was able to get the Grid Index tool to work. If the scale is too small and the feature it is based on doesn't have good coverage, then there won't be complete by the grid. Gonna have to mess with the scale or use a different feature. Once the grid is set up, the DDP feature functions great.
John