For the deer woods, I use a .375 Win with a 2x Bushnell scope...yeah, that's not much magnification, and I could only wonder as I paid for the scope if I was making a mistake or not. After some time at the range and in the field, I can tell you that I am very pleased with the 2x magnification for the deer woods for 100 yards and in. I have no reason to shoot over that here in the thick stuff of PA. Sure, there could be an opportunity for a longer shot, but it would still probably work. For groundhogs, my .222 carries a 3-12x Burris, which is ideal for groundhog hunting situations (longer shots). I like to make sure that my variable power scopes do not start off on the low side with too much magnification.
To answer your question, I think the 2x should do just fine, for the limited range that you plan on shooting at. Don't forget...the 2x is a bit easier to hold steady freehand when it's cold and you're shiverrrrrring too (at least that's from my experience with the 2x).