Answering questions deceptively or incorrectly is morally wrong, even reprehensible - at its worst, propaganda, for want of a better name - but is not illegal. But doing anything to interfere with the press, anything that could be reasonably construed as attempting to intimidate the press, is a straight-up violation of the First Amendment, and its injunction against the government "abridging the freedom of speech, or of the press". A press subject to government investigation for doing its job - reporting, being the press - cannot possibly do its job free of abridgment.
President Obama needs to do more than say he agrees with the above. He needs to root out the people in the Justice Department who abridged the First Amendment rights of the Associated Press. These abridgers need to be publicly denounced and fired.
Once again, in the attempt to safeguard our freedom, our freedom has in fact been abridged by our own government. As I've said many times over the years, the First Amendment is ever subject to equal-opportunity despoilers - meaning, trampling by government officials, of both parties. In the local governmental response to Occupy Wall Street in 2011, First Amendment rights of journalists and OWS participants were roundly violated by Democratic and well as Republican officials.
Press Secretary Jay Carney gave an eloquent statement of President Obama's devotion to the First Amendment at a press conference today. Obama now needs to follow through with actions.