The biggest issue is time: Each of the P90X workouts lasts approximately a hour and a half. For me that is about all the time I have for working out during the week. I get up around six in the morning and I don't get home from work until around six at night. At that point I don't really have the time to do more than a hour and a half of exercise, especially if I'm going to cook and/or do any type of cleaning. If I was the type that enjoyed getting up in morning and working out then it would be a lot easier to fit in multiple workouts during the day. Or if I won the lottery and therefore didn't have to work I could workout about three times a day. (A girl can dream....)
The second issue is soreness: Soreness isn't exactly the word I'm looking for but the point is that the workouts are fairly intense and you would need to plan on which days you're going to run so that you aren't in too much pain. The plyometrics and leg/back workouts are brutal on your legs so you probably won't want to run the next day. Now if you did a relatively short run in the morning of those workouts then that would probably be okay.
If you have the time then it should not be a problem to fit in running (or another exercise) in with P90X. If you are already pressed for time and barely fitting in your exercise then you probably won't have the time to do additional workouts with P90X. I really believe that the people that they show on the P90X infomercials are doing additional workouts (or maybe they just aren't eating chili-cheese fries).
In my ideal life I wouldn't be at work for 9-10 hours a day (not including the time it takes to get there) and therefore I would be able to get up in the morning and workout and then workout again in the evening without quickly becoming run down.
If anyone else has any thoughts on this situation then please feel free to comment.