These are perilous times, and our most sacred institutions are under full-scale assault — not in the Middle East, but on Tuesday’s prime-time TV lineup, where the U.S. Constitution and the concept of the situation comedy both get roughed up pretty badly.

As long as you’re not excessively attached to the First, Fourth, Fifth, Sixth or Eighth Amendments to the Constitution, the new CBS cop drama Vegas — a cross between Gunsmoke, The Untouchables and a Sheriff Joe Arpaio reality show — is wildly entertaining. If you’re more interested in a virtual-reality simulation of brain death, go with the Fox sitcoms Ben and Kate and The Mindy Project.

Vegas is set in 1960, just as the city was starting to exchange mobster fedoras for corporate three-piece suits. Dennis Quaid plays a key historical figure in that transition, Sheriff Ralph Lamb, who never allowed his enthusiasm for law enforcement to be diluted by lawyerly talk of civil liberties.

Vegas portrays Lamb as a populist everyman, a rancher who just wants to be left alone with his cows and tumbleweeds. But as growing gangland corruption spills in all directions, the mayor — knowing Lamb was a crackerjack military policeman serving overseas during World War II — drafts him for the vacant sheriff’s job.

Lamb’s approach to the job in no way resembles any of the nerdy CSI stuff you see on CBS crime procedurals. Warrants? Don’t need ‘em. Pesky defense lawyers? Lock ‘em up. Uncooperative suspects? Break a shotgun over their heads. That approach sets Lamb on an inevitable collision course with the new mob boss in town, Johnny Savino (Michael Chiklis). It’s not long before Lamb, backed by a squad of shotgun-toting deputies, struts through a casino floor to proclaim: “ I am the law here, Mr. Savino, and I will decide who’s breaking it.”

Vegas’ script, a marvel of button-pushing melodrama by veteran wiseguy chronicler Nicholas Pileggi, is fictionalized —but not nearly as much as you might think. The real-life Lamb once arrested 74 Hell’s Angels, tore up their motorcycles and gave them haircuts before releasing them, and his beatdowns of mouthy gangsters were the stuff of Las Vegas legend.

Quaid is riveting as Lamb, laconic but glowing with incandescent rage, a lit stick of dynamite with a very short fuse. Chiklis, who ironically owes his fame to playing a very similar rogue cop on FX’s The Shield, offers perfect counterpoint as a bemused gangster trying to calculate where Lamb’s bluster ends and his barbarity begins. In real life, Lamb once grabbed mobster John Roselli (the partial inspiration for Chiklis’ character), dragged him across a tabletop and slapped him silly while Roselli’s goons stood by, gaping.

Speaking of barbarity, Ben and Kate and The Mindy Project are best thought of as the lead offensive in Fox’s War on Comedy. Written without a scintilla of wit, peopled by characters who are variously dim and unpleasant, they’re mostly remarkable for their ability to continually produce affirmative answers to the question, could this be any worse?

Mindy Kaling, the Indian-American actress who has won a bunch comedy awards for her writing and acting on The Office that will now have to be repossessed and burned or at least exorcised, is the star and executive producer of The Mindy Project, which is probably too much guilt for any one human being to bear. She plays an obstetrician who imagines her life is a romantic-comedy film in which she’s destined to find the perfect guy, the testing for which entails sex on examining-room gurneys. Think Gray’s Anatomy with unpretty people; then think of something else to watch.

But don’t let it be Ben and Kate, which stars Dakota Johnson and Nat Faxon as emotionally blighted and intellectually adult survivors of their parents’ awful marriage who are now trying to raise Kate’s daughter from her awful marriage. If this doesn’t sound to you like a promising comedic premise, you’re way ahead of the game. Ben and Kate is sometimes shrill, sometimes belligerent and sometimes (well, a lot of times) merely stupid. It is never funny. “We’re like two peas in like the worst pod ever,” says Ben at one point. Let it be an epitaph, soon.