Consider this a companion piece to the earlier story coming out of the Texas legislature.  While a mob shouted down a vote on an abortion ban after 20 weeks, a National Journal poll shows a plurality of support for such a law among all Americans.  Furthermore, it gains a majority among all women:

Texas state Sen. Wendy Davis galvanized abortion-rights supporters–and even the White House–with a dramatic filibuster of a bill that would have outlawed all abortions after 20 weeks. But the latest United Technologies/National Journal Congressional Connection Poll shows that a plurality of Americans supports a ban on late abortions.

Americans favor such a bill by 48 percent to 44 percent.

Support was greatest among Republicans, 59 percent in support, but 53 percent of Americans not affiliated with either major party sided with the GOP. A majority of Democrats, 59 percent, were opposed while only 33 percent were in favor.

NJ warns that this issue could “fracture” Democrats, thanks to support from a perhaps-unexpected demographic:

Overall, the survey suggests that the 20-week abortion measure fractures some of the modern Democratic coalition. Among all age groups, it was young Americans–who have regularly sided with Democratic priorities in the age of Obama–who most strongly supported the measure (52 percent). The measure also received the support of 51 percent of white women, both those who are college educated and those who are not.

Among voters 18-29 years of age, the gap is 13 points at 52/39.  That is a key demographic, as this is the group that one would expect to be most impacted by abortion restrictions.  If younger voters support restrictions on abortion while the Democratic Party insists on nothing less than unrestricted abortion up to birth — the position staked out by the party during the House debate on the abortion restriction — their ability to argue that Republicans are extremist on social issues will dissipate.