I don't agree with everything this toon portrays; I just don't think Boehner is all that bothered by being manipulated in this fashion. Nor does most of the rest of the Republican party, for that matter.
Oh sure, there are exceptions -- even in Texas, like Bob Deuell and Jane Nelson -- but generally the GOP is more like Mike Pence and Jon Kyl: they want to force women to bear children and then starve both mother and child to death. They don't want to pay for their medicine and they damn sure don't want to pay for their education. And they will tell any lie they can think of to advance their cause.
But hey, elections have consequences. When we elect weak-ass conservative Democrats to negotiate with terrorists (declaring the resolution of the budget stalemate last night a victory, for example), we can't be too shocked about the outcome.