As jess20k stated, Mardi Gras people will be there anywhere from Feb. 2 - Feb. 10. Also, a cheerleading competition will be going on Feb. 1 - Feb. 3, and some of them may linger around a few days after that.
Although overall crowds won't be that bad during your week, I recommend going the last week in January to be on the safe side. I'll be there Jan. 26 - Feb. 2, so i'll hopefully be leaving right as the Mardi Gras and Cheerleader crowds kick in.
Good luck!