About 18 months from now, 1% of the world’s population will vanish. All that will be left of those people will be 65 million piles of clothing, “bereft of their occupants.” So much for an orderly first 100 days for President Hillary Clinton.

In “Hillary Agonistes,” Nick Salamone’s gutsy and inventive amalgam of Greek tragedy and ripped-from-tomorrow’s-headlines immediacy, something looking a lot like the biblical rapture has presented Madame President with a variety of hideous options. A terrified world watches mutely as she navigates these choices, making impressive leaps of logic as well as potentially calamitous missteps.

The remaining evangelicals are reeling from “the stigma that maybe the Lord didn’t want them.” (Video cameras have caught a panicked Pat Robertson shedding his clothes and going into hiding.) Adding insult to injury is the fact that Jane Fonda and — even worse — Bill Clinton are among the 65 million missing. Alternative theories quickly emerge, pointing the finger at everything from an anti-rapture instigated by Satan to alien abductions to an enormous Internet prank. Mr. Salamone chronicles the embattled president’s drift toward a sort of cautious zealotry in the ensuing days: Words such as “Antichrist” begin to creep into her public statements, and the building global turmoil threatens to finish what God or Satan or whoever has started.

Staged depictions of the rapture have traditionally been the province of schlocky thrillers starring Kirk Cameron, the born-again “Growing Pains” veteran. Not to be outmatched, Mr. Salamone has unearthed his own former sitcom star – Priscilla Barnes, best known as the third and final blonde on “Three’s Company.” Ms. Barnes goes well beyond the lowered vocal timbre and the unfortunate wig, offering a complicated and ultimately touching performance. Hillary Clinton’s blend of intellectual curiosity, self-regard, public travails, and ambition makes her as apt a subject for Greek tragedy as modern life has to offer, and if Ms. Barnes takes a while to tap into these divergent strains with equal aptitude, she finally rises to the challenge.

Mr. Salamone has also written himself several choice roles (along with a few duds) in “Hillary Agonistes.” As befits the play’s nods to Greek tragedy, both in structure and occasionally in syntax, he plays a series of men who nudge the protagonist toward terrible self-knowledge — while invariably advancing their own interests. Among these are Treasury Secretary Michael Bloomberg, scientific adviser Stephen Hawking (a potentially cheap laugh that actually yields a bracing discussion of the heresies that so often accompany scientific inquiry), and a cardinal who, liturgical differences aside, views the rapture as a welcome step toward heavenly transparency: “No one can blame Hitler or Mao or homosexuals or microbes for this one. … I think God is learning.”

Mr. Salamone’s attempts to interweave humor falter here and there, and some of his own broader characterizations don’t help on this score. Turning Chelsea Clinton (Rebecca Metz) into a burqawearing Muslim and peace advocate proves surprisingly effective, but the inclusion of an ominous force of darkness, complete with gas mask and spooky voice, gives the audience an all-too-welcome opportunity to put some distance between the play and its sobering messages. Lumpy and often undisciplined, “Hillary Agonistes” overreaches with a hubristic restlessness that would make its Greek forebears proud. If every Fringe Festival offering had the problems that it does, Lower Manhattan would be a lot more exciting right now.

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If this all sounds way too heavy for the Fringe Festival, “I Dig Doug” is eager — a bit too eager — to squeal its way into your heart as it plies its own brand of neon populism. In what could be best described as “Candide” as told to the YouTube provocateuse Obamagirl, a pair of celebutante wannabes (played by coauthors Karen DiConcetto and Rochelle Zimmerman) set off on a road trip from New York to the Iowa caucuses after one of them falls hard for a presidential candidate. The two women bring a tireless energy to this paper-thin picaresque — especially Ms. Zimmerman, who careens between playing the ditzy Nicole and everyone from a heartsick Waffle House waitress to the star of Fox’s latest reality-TV entry, “My Perfect Millionaire Prince Charming Unmasked! Honolulu: Season II.”

That title, ghastly and almost plausible, gives a sense of where “I Dig Doug” sits most comfortably: Everyone from Zac Posen to that diaper-wearing astronaut lady is name-checked, and director Bert V. Royal spotlights the surface charms of his protagonists faster than you can say “Elle Woods.” But as the road trip winds through West Virginia and Kentucky (wait, Daddy’s car doesn’t have G.P.S.?), the buzz soon dissipates. The maturation of Ms. DiConcetto’s character is underdeveloped, too many comic vignettes taper off just as they’re finding their rhythms, and a pair of unconvincing trick endings add little to “I Dig Doug.”

Just as “Urinetown” illustrated the commercial potential of conjoining political savvy and bratty wit, its many, many hapless successors have demonstrated just how tough the two are to balance. If making 65 million people disappear or destroying the world’s population in a Malthusian catastrophe (as in “Urinetown”) is what it takes, so be it.

“Hillary Agonistes” until August 22 (107 Suffolk St., between Rivington and Delancey streets); “I Dig Doug” until August 24 (15 Vandam St., between Sixth Avenue and Varick Street). Call 212-279-4488 for all tickets.