But the way the Republican campaign is going in South Carolina is raising an even bigger question, not just for Cruz but for the party as a whole: Can anybody win this thing?

Welcome to the great Republican stalemate. No candidate commands anything approaching a majority of the primary electorate. Trump, in first place, pulls about one-third of the vote. All the candidates are locked in their narrow, mutually exclusive “lanes” of different kinds of voters. And rather than back down or seek accommodation, they keep upping the ante.

The paralyzed state of the field has even raised the possibility that no candidate will have a majority of delegates when the Republican convention opens in Cleveland in July, forcing a second ballot and a chaotic fight on the convention floor. The idea of a contested convention, perennially batted about but usually a rules-nerd’s pipe dream, seems a distinct possibility this time around.

The primary, in other words, is just as gridlocked as Washington, where bills can’t get passed and the Supreme Court can’t make decisions. A majority of Republican voters value standing on principle more than compromise; they see gridlock as the only bulwark against tyranny, and refusing to back down as the mark of character. Now that attitude has come to the political campaign, with six remaining candidates who swear they will never yield, and a party so divided its factions may be fundamentally irreconcilable.

But back to Saturday’s debate, in which Trump was booed for saying George W. Bush knowingly lied about weapons of mass destruction in Iraq; Marco Rubio said Cruz had a “disturbing pattern” of “just … telling lies”; Trump called Jeb Bush weak and a liar and Cruz “the single biggest liar” and “a nasty guy”; and Bush said Trump was the weak one, and disinvited him from an upcoming rally with the former president. Trump shot back, “I don’t want to go.”

Midway through the debate, the GOP message maven Frank Luntz tweeted, “Seriously, this is insane. The GOP is destroying itself tonight, and they have no one to blame but themselves.” On Thursday, I ran into Luntz in the press area of a Rubio town hall in Anderson. He looked depressed. He’d seen tough elections before, he said, but this one was “poisonous,” and would send independent voters fleeing to the comparatively civil Democrats.

As Luntz spoke, Rubio’s campaign was straining mightily to gin up controversy over the Cruz campaign’s creation of a website attacking Rubio for his position on trade—a position Cruz had once shared. The site featured a stock photograph that had been altered so that it seemed to show Rubio and Obama shaking hands. Rubio’s adviser, Todd Harris, was passing out paper copies of the photo and seething that it was a “deception” that proved Cruz was “desperate.”

Despite the conventional wisdom that Cruz is an “outsider” candidate and Rubio an “establishment” one, Rubio’s campaign has long believed Cruz’s voters are susceptible to being peeled off. Rubio representatives can frequently be found outside Cruz events, handing out fliers accusing Cruz of supporting “European style taxes” or plastic pocket calculators labeled “Ted Cruz: Political Calculator,” accompanied by a sheet detailing Cruz’s alleged reversals.