From left, Yara Martinez, Mark Consuelos, Clark Johnson and John Goodman in a scene from Amazon Studios series “Alpha House.” (Amazon Studios)

Garry Trudeau’s “Alpha House,” a half-hour comedy series that’s now streaming for your fickle platform pleasure on, is about four Republican senators who are roommates in a Capitol Hill townhouse.

Everything about “Alpha House” looks good to go at first. It has the right cast, led by John Goodman; it has a studied understanding that modern comedy must put abject humiliation and awkwardness above all other forms of humor; it is written so that characters speak in smart spurts of cutting hatefulness; it easily accommodates a series of boldface names who make cameo appearances as either characters or as themselves; and most of all, it has at its helm Trudeau, the “Doonesbury” creator who can lay claim to a formative work of TV political comedy (HBO’s ancient “Tanner ’88,” a collaboration with Robert Altman).

Strangely, the one element “Alpha House” is missing is hilarity.

As in LOL, as in the kind of laughter you can hear coming from the person in the other room who is watching the show on his iPa — excuse me, his Kindle Fire. (Obligatorily, I must note here that The Washington Post is now owned by the guy who founded Amazon. But you know that.) The show is so tight — maybe too tight — that it starts to choke on its own power-tie premise in the first three episodes.

Part of “Alpha House’s” burden to bear is that it feels about 15 crucial minutes late to the raging bonfire that is now Washington parody. This territory is already well-scorched — lately by HBO’s cruelly unerring “Veep,” but also by Netflix’s stylish and utterly cynical “House of Cards” (meant to be a drama, yet easily ingested as satire, like ABC’s “Scandal”), as well as the familiar, nightly whippings that Beltway and media culture receive from Jon Stewart and Stephen Colbert.

A more pressing challenge (perhaps also a boon) to launching yet another show about Washington’s absurd ineptitude is that you have to compete with actual headlines, including but not limited to debt ceilings, shutdowns, partisan gridlock and, of course, federal Web site rollouts. There’s never been a better time to strike, except for the long line of people already doing it. The mockery of This Town — as portrayed in the best-selling book “This Town” — can easily get as old as the subject being mocked.

Colbert, whose show factors into one of “Alpha House’s” establishing plots, is kind of a spirit guide for “Alpha House,” which, like “The Colbert Report,” sends up Republican politics with characters who are themselves unwaveringly Republican.

Thus we enter a somewhat nuanced and sarcastic exploration of greed, piggishness and double standards on social and sexual mores — all of it played for laughs rather than outrage.

Goodman is North Carolina Sen. Gil John Biggs, a profane politician coasting mainly on his former glory as a basketball coach, which has guaranteed him a long life in Washington — or so he thinks. His roomies include the townhouse’s fussy owner, Sen. Louis Laffer of Nevada (Matt Malloy), a married Mormon struggling to maintain appearances (the viewer is to understand that he’s a closet case hiding his homosexuality). Laffer’s reelection has turned into an uphill battle now that he’s facing a primary race against a macho, gun-toting rival; Biggs, too, is facing a serious challenger and must reluctantly rediscover his dwindling charm reserves.

Meanwhile, Pennsylvania Sen. Robert Bettencourt (played by “The Wire’s” Clark Johnson) swaggers along a fine line: He’s a powerful black Republican whose gift for graft has him going before grand juries and the Senate’s ethics committee. Lastly, the senators are joined by a new housemate who can outshine and out-slime them all: the freshly divorced, skirt-chasing Florida Sen. Andy Guzman (Mark Consuelos), whose invincible sense of entitlement has him eyeing the White House.

Through these four men, Trudeau and company have landed on a set of updated, if nevertheless derisively stereotypical, portrayals of GOP hubris — as when the four senators make a publicity trip to Afghanistan and are compelled (through PAC contributors) to entrust their safety to a private-sector paramilitary escort instead of the U.S. military.

The most interesting (and pathetic) character is Malloy’s Sen. Laffer, who can’t catch a break: A self-effacing trip to “The Colbert Report” suddenly devolves when the TV host challenges Laffer to a wrestling match; he winds up with a face full of Colbert’s crotch.

Like Julia Louis-Dreyfus’s vice president on “Veep,” the men of “Alpha House” each struggle to keep ahead of the Twittersphere’s light-speed effect on political currency; Goodman says that something has “gone virile” online; Laffer has to call a staffer to ask what a “meme” is. It’s all a little bit funny, but, again, it’s not the sort of funny in which you repeat the best lines to your friends.

The way the “Alpha House” men go about business on the Hill could be interpreted as flattery to the Republicans (especially in the Goodman character’s unabashed confidence in his conservative views), perhaps as much as it can be seen as the insult the show ultimately intends to be. After all, Trudeau and company are promoting the party’s fondest big-tent desires: Here's a black guy, a gay-ish guy, a Latino guy, a fat Southern guy — it’s all the elephants in one room, sharing rent.

In this age of constantly morphing rules about publicity and shame, the Republicans should know exactly how to treat “Alpha House”: as a Valentine.

Alpha House

(11 half-hour episodes) streaming at Episodes 1 to 3 are free; weekly episodes will follow via Amazon Prime.