The reference is to what is essentially the Reagan coalition of Economic conservatives, foreign policy hawks, and social conservatives. Many of us fit comfortably in all three categories, but the successful coalition means including people who may only fit on a couple of the legs. Go back 40 or 50 years and the coalition was only of the first two. Reagan managed to bring many Catholics and southern and western and otherwise rural evangelicals along and that has made the difference between success and failure. As with any coalition, there will always be some tensions. Huckabee just didn't appeal to all three legs and hence couldn't pull it off (plus his abysmal ignorance of foreign affairs became too obvious). Thompson probably had the most appeal across the board, but came in too late and too disorganized. He best articulated the coalition, however.
Thank you for the broader explanation.