The thick skin is probably required more often when delaing with your own firm's supervisors, managers and partners. Your entire Big 4 experience will be determined primarily by two things - your mentor (how much support they provide you) and the caliber of your client - if they can provide you the material you requested on schedule. A bad client and unsupportive mentoring (from either your designated mentor or another Sr. Manager/Partner) will, without a doubt, cause you to leave the firm withing 3 years tops.
Even if your mentor likes you if they have a falling out with their mentor and leave the firm then you are most often going to do the same. For all their professed businerss expertise there are precious few high-quality competent personnel managers at Big 4 firms.