A new poll (PDF) from Hart Research, a firm founded by respected Democratic pollster Peter Hart, shows widespread opposition to defunding Planned Parenthood. By a 64-28 margin, registered voters are against ending government funding for PP, an organization which is viewed positively by 55% (and negatively by just 25%). Democrats, as you'd expect, are most opposed (86%), but independents are as well, by a very broad 64-29 spread.
Republican, of course, are a whole different story:
Teabaggers are most in favor of defunding Planned Parenthood, at a pretty wide 33-63 margin - they're almost as supportive as independents are hostile. So you can see why the GOP leadership seems prepared to crucify itself on this cross of scold: their base will want to tan their hides if they accept any compromises. (And note that according to the memo, this "base" comprises almost two thirds of the party.)
But the men (and it pretty much is all men) in charge of the Republican Party know exactly whose in charge of them—and it's David & Charles Koch, not a bunch of weirdos who like to dress up in Revolutionary War uniforms. So as long as they get whatever it is their corporate masters require, I'd expect the GOP honchos to sell out their loudest, mouthbreathing-est supporters on this issue, despite what this poll says.
And if they don't, and they go ahead and force a government shutdown because of Planned Parenthood, they are going to piss off the entire rest of the country.