Yes, there is some joking about "post natal abortions" for certain extremist politicians, but it's never serious about permitting after-birth abortions".
FYI, "anti-choice" is a pejorative, as is "pro-abortion" for pro-choice people. Let's steer clear of mudslinging on such a controversial topic, so as to avoid a flamewar. :)
It's less pejorative than the implication that "pro-life" connotes that the opposition is "anti-life". Few pro-lifers seem to put any effort into guaranteeing life for anybody -- often in favor of capital punishment, and practically never advocating policies that preserve life such as health care.
"Anti-choice" is about the most dispassionate, accurate label I can apply. There is a choice that the wish to deny. Any other term is a euphemism.