Jonah & Mark, to my knowledge, government officials who are not in law-enforcement are not obliged any more than any other people in the United States to report a bribe. The pertinent law here (as Jim Lindgren notes in the post cited by Mark) is “misprision of a felony.” This crime has been on the books forever but it has never been embraced in the United States. Currently codified at Section 4 of the federal penal code (Title 18), it states:
Whoever, having knowledge of the actual commission of a felony cognizable by a court of the United States, conceals and does not as soon as possible make known the same to some judge or other person in civil or military authority under the United States, shall be fined under this title or imprisoned not more than three years, or both.
If we were dealing only with the plain language of the statute, all that would be necessary for conviction would be for the prosecutor to establish that (a) a felony actually had been committed, (b) the defendant knew that felony had been committed, and (c) the defendant failed to report that felony to the authorities. But — leaving aside such deep epistemological questions as “do I really know anything” — this would turn all of us into criminals since, at one point or another, everyone knows of some crime that he fails to report. So misprision has always required more, namely that the defendant not only knew about the crime but took affirmative steps to help conceal it.
This is why misprision is so rarely prosecuted. A person who takes affirmative steps to conceal a crime can usually be prosecuted for that crime itself, either as an aider and abettor, a coconspirator, or an accessory after the fact. Those crimes are all easier sells for the prosecutor — juries don’t like convicting someone for failing to snitch unless the failure involves something truly heinous, like a murder or a terrorist attack.
One last thought: I am referring above to the non-political context of prosecution. By contrast, I would think misprision would be a perfectly good reason to impeach a political official. And if the official was not an office-holder but a staffer of the president (the chief executive to whom the Attorney General and all U.S. attorneys report) it should be a firing offense.
But all that said, I don’t think a political official has a special legal duty (as opposed to moral, ethical or political duty) to report a crime. And, sadly, I suspect if you tried to prosecute a political official for failing to report an attempted bribe, the official’s defense would be: “I didn’t look at it as a bribe; I looked at it as the horse-trading that goes on everyday in politics — the nature of it doesn’t change just because the FBI happened to capture it on tape.”