Here’s a story about a little boy named Pierre, who stars in Maurice Sendak’s classic children’s tale. Pierre is an obstinate brat who sits backward in his chair, pours syrup on his hair, and screams, “I don’t care!” at every kindhearted word from his parents. When a lion shows up and asks him if he’d like to die, Pierre ignores the obvious danger and blurts, “I don’t care!”
The lion eats him.
With midterm elections on the horizon, the Republican Party should be hyper-attuned to its weak standing among nonwhites, women, and young people. Instead, its Pierre wing — hard-right purists — insists that the GOP’s problem is a shortage of obstinacy. Block immigration reform and risk alienating Hispanics? “I don’t care!” Be seen as intolerant of gays and perform badly among young voters? “I don’t care!” Demand that moderates be purged from the party and continue to lose elections in swing states? “I don’t care!”
The most visible case is the Tea Party-backed campaign — supported by 17 senators and 77 members of Congress — to shut down the government rather than vote for a budget that funds Obamacare. With Democrats controlling the Senate and the White House, it’s an empty threat. But experience shows that talk of government shutdowns hurts Republicans, whose standing with the public could hardly sink further. The latest Quinnipiac poll gives congressional Republicans a pathetic 19% approval rating.
“Why pick a fight you can’t win?” asks Oklahoma Rep. Tom Cole. The prolife, NRA-loving Cole is about as conservative as they come, but he’s also a pragmatic and experienced electoral strategist, and he fears this latest crusade is damaging a GOP brand that is already “in the toilet.”
The Tea Party response: “I don’t care!” One hard-right talk-show host denounced Cole as a “cream puff.” Other sane GOP voices, like John McCain and Bob Corker, have called the campaign “dumb” and “silly” — but Tea Party activists are trying to punish those kinds of Republicans with primary challenges. “If they fund it, they own it,” the activists tell a conservative base that passionately hates Obamacare.
The purity campaign goes beyond tactics. Conservative darling Marco Rubio has drawn boos at events for leading immigration reform; now he rarely addresses the subject, admitting that “politically, it has not been a pleasant experience.” Voters in both parties overwhelmingly support immigration reform. They also tell pollsters they are tired of obstructionist politicians. But that hasn’t stopped Tea Party activists from urging Tennessee Sen. Lamar Alexander not to run again because “our great nation can no longer afford compromise and bipartisanship, two traits for which you have become famous.”
The party’s Pierres would do well to recall that Republicans lost the chance to pick up three Senate seats in 2010 — and dethrone Harry Reid — because of weak Tea Party candidates. In 2012 the party failed in two key Senate races after offensive comments about rape by Todd Akin in Missouri and Richard Mourdock in Indiana. In the House, Tea Party hero Allen West lost and Michele Bachmann barely squeaked by.
In 2014, electoral tides mean the GOP should hold on to the House and perhaps even capture the Senate. But that’s assuming the Republican brand doesn’t suffer more. As congressional analyst Amy Walter of the Cook Political Report puts it, “It’s very hard for the Democrats to win control of Congress, but Republicans can lose it.”
Cole attributes the Pierre behavior to political immaturity: Most Tea Party-backed members of Congress haven’t been around long enough to appreciate the strength of the Democrats. “They assume we’re smarter and more courageous than our opponents,” Cole tells me. “Well, the Democrats are smart too, and they control the Senate and the bully pulpit of the White House. The idea that they are going to collapse is foolish.”
By the way, Pierre survives in the end — but only because grownups come to his rescue.
This story is from the September 16, 2013 issue of Fortune.