Confirming every previous poll taken on the subject in the last 50 years, the Huffington Post has a poll out today showing that Americans don't approve of late term abortion. In fact, they don't approve of abortion period. 49% consider the practice itself morally wrong, while only 12% consider it morally acceptable (nauseatingly, another 24% don't consider it a moral issue at all).
The really confusing thing, and the only saving grace for HuffPo's absurdly leftist readers (see embedded poll comparing overall vs reader responses) is the seeming contradiction between respondents personal opinion about abortion and their allowance for the decision to be between the woman and her doctor (63% support).
However, the likely reason for this apparently conflict is pure political correctness. When confronted with the question of whether a medical decision should be between a patient and doctor, or a government dictate, the vast majority of people will allow the individual decision. This is reflected in constant political rhetoric about healthcare in general.
However, the validity of that question is undermined by the rest of the poll. While only 26% say the government should pass restrictions on abortion, 59% (!) favor a federal (!) ban on abortion after 20-weeks, 43% think there aren't enough restrictions on abortion, and only 19% think abortion should always be legal. If 63% of the country really thought the decision should be only between the woman and doctor, then that same 63% would say it should always be legal, otherwise it's not just between the woman and doctor.
But Americans are notoriously inconsistent. Or at least they usually are. On abortion, they're remarkably consistent. Almost no one thinks abortion should always be available to anyone no matter what. That's what is going on in places like Texas and North Carolina, not "extreme anti-choice" radicalism.