shouting head
n. A loud and aggressive person, particularly one who is a television pundit or commentator.
Other Forms
In March, Bill O'Reilly, shouting head for Fox News, demonstrated his absolute certainty that Americans would find weapons of mass destruction in Iraq by declaring on "Good Morning America," "If the Americans go in and overthrow Saddam Hussein and it's clean, he has nothing, I will apologize to the nation, and I will not trust the Bush administration again."
—Jonathan Chait, “News Guarantees,” The New York Times, December 14, 2003
We have the media disclosing, in short order, that the woman in the Bryant case overdosed on drugs in May and three months earlier was hospitalized when authorities deemed her a danger to herself.

And that's before we get to the hordes of reporters staking out the woman's home, the National Enquirer dangling big bucks, and the lawyers, former prosecutors, sports agents and other shouting heads who are boosting the case to O.J. decibel levels.
—Howard Kurtz, “Naming names,” The Chicago Tribune, July 29, 2003
1983 (earliest)
But the crucial thing about "Blood Feud" is that one may dismiss its interpretation of history as Hollywood hooey (not that the theories about Mob complicity and Mob-CIA ties are undocumented elsewhere) and still find all four hours gripping, electric and on some useful level disturbing, in part because writer Boris and director Michael Newell keep a taut, taut ship and largely because, as Kennedy and Hoffa, actors Cotter Smith and Robert Blake are sensationally strong and consistent.

They are required to storm through confrontation after confrontation (this is not "talking head" television so much as shouting head television) including some that probably never occurred.
—Tom Shales, “'Blood Feud': Jousting In Camelot,” The Washington Post, May 11, 1983
This phrase is the loudmouth version of a talking head, "a person, such as a newscaster or pundit, talking on television while shown in a close-up shot," an epithet that entered the language around 1976.