Some 23 percent say abortion should be legal most of the time, but with some exceptions, and the 35 percent who felt it should be illegal except in circumstances of rape, incest and to save a woman's life. About 40 percent of respondents said abortion should be wholly legal (31 percent) or illegal (9 percent).

Groups on both sides of the argument defended their causes to mark the anniversary.  

"As the nation's leading women's health care provider and advocate, Planned Parenthood understands that abortion is a deeply personal and often complex decision for a woman to consider, if and when she needs it," Planned Parenthood President Cecile Richards said in a statement. "A woman should have accurate information about all of her options around her pregnancy. To protect her health and the health of her family, a woman must have access to safe, legal abortion without interference from politicians, as protected by the Supreme Court for the last 40 years."

Meanwhile, pro-life organization National Right to Life was encouraging "right-to-life activists from coast-to-coast to redouble their efforts on behalf of mothers and their unborn children."

"Abortion-on-demand, which has claimed the lives of more than 55 million unborn children, has remained the law of the land for 40 years," said Carol Tobias, president of National Right to Life. Roe is a sad commentary on our society's attitudes toward women and their unborn children. Instead of helping and empowering mothers, our society funnels them to the nearest abortion clinic.

The WSJ/NBC survey was conducted Jan. 12-15 and has a 3.1 percent margin of error.