The basic underlying concept in privileged communication is the right against self-incrimination, the Fifth Amendment of the Bill of Rights. The assumption is you will tell your spouse, your lawyer, and your minister everything under the expectation of confidentiality. The prohibition is not a protection for said spouse, lawyer or minister; it is a protection of the rights of the suspect. The state may not compel these groups to testify. These privileges are also found in English Common Law.
Lawyers are officers of the court, which means they may not be compelled to testify about information they have about past behavior, but they must report information to prevent future crimes.
In some jurisdictions not only may these classes not be compelled to testify, they may not volunteer to testify.
Note that the privilege is prevent information from being revealed by people who are known. The claim to press privilege is based on preventing people from being revealed after the information is published. The claim is also based on the First Amendment, not the Fifth.
In the case of Cooper and Miller, they are claiming that their status as reporters should be privileged. The argument is that without the ability to shield sources, they would be unable to gather the news. I could point out that the media has no idea whether or not they can gather the news without unnamed sources because they make little effort to do so with such sources.
While it is all well and good to point to the Pentagon papers and Watergate as examples of stories that began with sources, and there are any number of stories of corporate malfeasance that began with "whistle blowers" as justification for this claim, no right is absolute.
Bob Novak revealed that convicted spy Robert Hanssen was one of his sources for several stories, and Newsweek
famously outed Oliver North as the source of several leaks, after North attacked the media for printing leaks. This would indicate the media doesn't hold to the concept of absolute protection of sources.
Some have noted that those in this case have not seen the evidence filed by the prosecutor. What lawyerly piffle. This matter is before a grand jury and all grand jury testimony is secret to protect people if there is no indictment. That some prosecutors choose to "leak" to the media and the media chooses to print those leaks doesn't alter the fact that the testimony is secret.
Freedom of the press means the press is free to print whatever it wishes without prior restraint; it does not mean the press is not responsible for what it prints. The press has extra protection from libel suits, but it can still be sued.
I might have more sympathy for these people if they had supported Susan McDougal when she was jailed for refusing to cooperate with "The Starr Chamber" or had actually done a little reporting of the facts in the last decade.
The question is simple who is the victim? Is the "victim" the government or a faceless corporation that has been exposed as incompetent or criminal? No, the victims are a "whistle blower" and his wife. This is not a case of the media serving the general good; this is a case of the media cooperating with the government to punish an opponent of those in power.