Must criticism of a public official be true to be protected by the First Ammendment?
There are two areas of law that could be involved in this question, Constitutional law and the law of defamation. The First Amendment prevents the government from suppressing most speech, and the law of defamation concerns harm to a person's reputation, harm for which one may sue for damages.
The central issue under the First Amendment in this context is whether the government can stop a person from criticizing a public official, and the short answer is that it cannot. In order to do so, the government would have to seek an injunction to halt this, and this is a non-starter. The only time the government is able to prevail is probably going to be in the interests of national security, for example, someone who had advance knowledge of the plan to capture or kill Osama bin Laden, someone who wanted to criticize a public official about this plan. Aside from a rare instance such as this, we can say whatever we like about our public officials and the First Amendment is what gives us that right. What we say may or may not even be true insofar as the First Amendment is concerned. This is our constitutional protection from the government.
Defamation, on the other hand, has nothing to do with controlling the actions of government against us. Defamation is a tort, a harm to a person that can result in lawsuit filed by the defamed person, with the defendant having to pay monetary damages and/or having to cease and desist the defamation. Defamation is the act of saying or writing something untruthful about a person that causes that person's reputation to be harmed. Written defamation is referred to as libel, and spoken defamation is referred to as slander. If, in our criticism of a public official, we say or write something untruthful, something that damages the public official's reputation, we can be sued for defamation. There is more latitude afforded for criticism of public officials, though, than for private individuals, and a certain amount of vague hyperbole is not generally viewed as defamatory in the law. For example, if I call my senator a scoundrel, my senator is not likely to prevail in a defamation suit. However, if I call my state senator a thief or a womanizer, I need to be prepared to establish the truth of those statements.
It is important to understand that these are very different bodies of law when we wish to speak or write about public officials. As long as we are truthful, we need not worry about being sued for defamation, and as long as we are not compromising national security, we need worry about nothing at all from the hands of the government.