Sharing with her Fortune magazine readers the Maurice Sendak story of a petulant buy named Pierre, whose “I don’t care” attitude leads to his untimely demise, Nina Easton draws parallels with those conservatives in Washington who toy with the notion of forcing a federal government shutdown.

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 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.”