You said you cheated because you became "egocentric and narcissistic." Who wouldn't understand that a selfish, self-loving man put his primal desires above all things he professed to believe in, like morals, family and religion?
As long as you admit you were only thinking of you, I'm okay with it.
You said you "took responsibility" with your family. "Yes, honey and my church-going children, remember when I denounced Bill Clinton for screwing around on Hillary and making her fodder for all the media? Well, the John Edwards that you are going to see all over the newspapers, the one that is going to lose his chance to be vice-president because he supposedly had a torrid sexual affair with a woman named Rielle Hunter? I'm responsible for that, that's me!" You 'fessed up. That's all any woman would need, especially a woman who campaigned alongside you while delaying treatment for her chronic cancer so she could assist you in your attempt to be president. As for the kids, I'm sure your "responsible-ness" will be enough for them too...they'll never hold it against you even after their dear mother leaves this earth.
You said, "She was in remission." John, I can relate. My husband battled testicular cancer. It was an incredibly emotional and scary time for my family. During this period we watched someone we love endure chemotherapy and two surgeries, following a protocol that comes with lots of pain and discomfort and no guarantees...all the while looking into the eyes of two wonderful children and promising everything will be alright. So John, I can see that when you got the news that the spouse you love is in remission how your thoughts would wander to celebrating by making love with someone else.
You said you "made a serious error in judgment and conducted [yourself] in a way that was disloyal to [your] family and to [your core] beliefs." No problem. One's core can be a confusing thing. Just 'cause you believe, at your core, that others shouldn't be unfaithful, doesn't mean that applies to you. Plus, admitting to a "serious" error is so much more satisfying than admitted to a "little error."
You also said "[we] cannot beat [you] up more than [you] have already beaten up [yourself]. " Here, I think you may be wrong, but I give you credit for beating yourself up. Did you happen to use a red hot poker by any chance? Did you squeeze your own nuts till you were singing soprano and turning blue? If your answer is "yes," then as I said before, "John Edwards, I forgive you."