First Amendment experts note that while the media could be prosecuted for publishing Trump's tax returns, a news organization could also assert a First Amendment defense. In the case of the Pentagon Papers, for example, The Post argued that publication served an important public interest.

But those arguments would not be sure winners, experts said. And members of the media would need to consider risks to their sources in any investigation of who shared Trump's tax information.

"The courts could say, if the public thinks the tax returns are so important, let it demand that the candidate authorize the IRS to release them on pain of losing votes," said Jonathan Zittrain, a privacy expert and professor at Harvard Law School.