As seen in the Wall Street Journal (free link today):
The latest telephone survey of 1,016 adults indicates Roe v. Wade is supported by a slim 49% to 47% plurality, compared with 52% who favored the decision in 2005 (see poll) and 57% in 1998.
Despite apparent waning support, a substantial majority (63%) of those polled don’t think it is likely that this Supreme Court will overturn Roe v. Wade over the next few years.
However, 40% of those polled favor laws that would make it more difficult for a woman to get an abortion, while another 40% say no change should be made to existing abortion laws, and 15% favor laws that would make it easier to get an abortion.