The story on Edwards and his affair is not the affair, persay. Many politicians have affairs and even get caught and still live on politically. Many republican and many democrat. What will kill Edwards's political career:
1) Many believe Edwards traded on his wife's condition in order to gain in the primary campaign. It is one thing to cheat on your wife while she's sick, it is another to be as craven as to both kick her to the curb with the affair and to trade on her poor health to your political benefit.
2) The coverup. Many cheating politicians are found out. But relatively rare is it for a politician to survive extensive or expensive coverups. In this case it appears there has been in the area of 2-5 million dollars paid to keep this bottled up. The people involved beg questions of campaign finance violations. The amounts involved beg questions of IRS violations. The 9-12 month long "investigation" of this whole thing and the denials that were made until recently are at issue.
3) The hiring. The woman was hired to do web documentaries of Edwards on the campaign trail. She had zero qualifications and history of doing such things and was paid a very nice salary for it. Also the timing of the hiring vis a vis the start of the affair has come into question.
4) Paternity. Some of the before mentioned alleged coverup money may be to make sure the woman doesn't get a paternity test. Cheating is one thing, having a kid is another, denying the kid as your own (and all the financial and social benefits that come along with it) while paying off the mother to deny paternity testing while you parade around inviting the testing is quite another.
5) Hillary. There is a great deal of bad blood in the democrat party with regard to how Hillary was treated by Edwards and Obama in the primaries. While I think the polling and voting trends don't necessarily prove it out, there will be many that blame Edwards' campaign for sapping away Hillary voters and causing her to lose the primaries in the earlier going when it would have counted a lot.
6) Undeniable is that Edwards was having this affair while campaigning for his party's nomination for President. This speaks to a horrible sense of judgement and calls into question his loyalty to the party. Would he have won the nomination or been selected for VP, and then this news come out, it would have been a crippling blow to the campaign and the party this election. The specter of it is enough to consider him unelectable in national democrat politics ever again.
7) Many democrats and almost all republicans disliked Silky anyway, and this whole thing just entrenches it. He was toast before this happened, really. This just puts him into the vaunted group of "post toasty" former politicians.
8) The woman. Not to be too politically incorrect, but she's a loopy chick. A book was written with a character based on her that detailed how "classy" she was. Maybe no one really puts his choice past him, but that doesn't mean people don't hold his horrible taste in adulterous companion against him. I know I do.
9) And he went back!? Edwards knew people were onto this whole thing, and he had the balls to actually visit her again, supposedly well after the affair has ended. Just stupid, stupid, stupid.
That all said, he has a future as a lawyer, maybe local politics, or perhaps as a political appointee. He'll be fine, assuming he didn't do anything illegal in all this.