Did John McCain screw up by saying he screwed up?

We underlined how McCain's hesitations to suspend his campaign were a turning point after what he lost his credibility. His canceling his appearance on the Late show was the worst idea his campaign had, since they gave the opportunity for David Letterman to make fun at him by pointing he stayed in New York... McCain had obviously to move on... But I wonder how many people work in his campaign? And how many hours did they waiste to build different strategies, to find out some excuses, to devise some unbelievable stories and to end up making up this move: go back on the Late show, make no explanation, no excuse, just say: "I screwed up" and hope it will work?