So the National Enquirer is reporting that President Obama is having/had an affair with a staffer... at first blush, I find it credible. When you consider how blind the press was to John Edwards' affair, it's easy to imagine the mainstream media covering up an affair by Obama. We'll have to see all the evidence, but I won't be shocked if it's true.
Some people are eager to dismiss sexual affairs as "private" matters that shouldn't be considered when evaluating politicians. Others (such as myself) believe that marital infidelity reveals a fundamental character flaw, and said flaw will also manifest itself in the political realm in ways that may not be directly visible. I.e., if you cheat on your wife, why should I trust you not to cheat on me as a citizen?
But I think there's an even more important consideration: national security. From this angle, it isn't the affair that's important, it's the fact that the affair is an embarrassing secret. Secrets provide leverage to be used by enemies, and not just personal enemies but national enemies. If an enemy of the United States were to discover that the President is having a secret affair, there's no telling how much damage the enemy could inflict in the form of concessions, espionage, theft, political appointments, vetoes, and so forth.
Note: affairs that aren't secret don't carry this same danger. If an affair is common knowledge then it can't be used as leverage. At that point, it's "merely" an issue of character and trustworthiness.
If President Obama were having a secret affair, I think it would be prudent to impeach him immediately on national security grounds. Breaking trust and having poor moral character are bad, but I see those as issues that can be sorted out by voters via the election process. Endangering national security for personal sexual gratification is a much more serious matter.