If you were a football coach and one of your players looked for a reporter at half-time so he could criticize other players on the team, complained that your strategy is all wrong, and generally told everyone listening that the team deserves to lose, do you think he'd be on the bench the next week? Do you think he'd have a job at all?
Whether you agree with Ted Cruz and Mike Lee (I do) or not, they had a strategy they wanted to pursue. They started by pushing to defund Obamacare and from there, the GOP was supposed to negotiate Obamacare compromises.
John Boehner apparently thought that strategy made enough sense that he decided to pursue it.
Has he executed it particularly well? No; after a brilliant start, Boehner seems to have quieted down and lost focus. That's frustrating because the GOP can win this fight with the public while firing up its own base any time it wants. As Dick Morris suggested,
End the shutdown immediately by passing a continuing resolution to fund the government EXCEPT that the subsidy lawmakers get for health insurance should be ended. The public will applaud this and God grant that Obama is dumb enough to oppose it!
Let the Democrats go out and defend shutting down the entire government day after day to protect their exemption from a law they're forcing on the rest of the country. Let them explain why they deserve to have 75% of their Obamacare fees paid by the taxpayers, while tens of millions of Americans are paying more money they can't afford for a service they don't want in the first place. The Republicans already voted for that once when they knew the Democrats would reject it; so when they can actually win this whole fight if they want to put it forward again and stick to it, why are they refusing to pull the trigger? A lot of people are going to suspect that the real question here is whether the Republicans would rather win this fight politically or whether they'd rather lose and keep their Obamacare subsidies. There's no question which decision would be better for the Republican Party, the country, and for the long term prospects of getting rid of Obamacare. So the question now is why aren't they doing it?