Wow, Sabbykay! I've never had any constipation problems from cheese. Each body is different, though, and what Suzanne says is true (as always!
): you need to follow what works for your body.
However, SBD is very different from Atkins, especially in the amount of high fiber foods you're allowed to eat. Constipation still happens, but I don't think cheese is usually the culprit. Make sure you eat beans (Kara's right...), bell peppers, and tomatoes to help you get through the detox in P1 with less symptoms. The fiber will also help the constipation. Make sure you get lots of water and when you get to Phase 2, consider adding items like Fiber One to your diet.
Exercise also helps constipation a lot! If you aren't used to exercising much, don't start in Phase 1...it's really tough to do that. But if you've already been exercising a lot, it's fine to continue in P1.
I find SF Fiber Choice tablets to be very helpful, as are over-the-counter stool softeners. Metamucil works too, though some find it to cause gas. Just try things and see what works for you!