Restrictions like partial birth abortions and parental notification? Yes, I agree with you.
There was another poll from 2003 from a different pollster that showed a similar result.
I believe your comments here reflect public sentiment from perhaps 15-20 years ago, but no longer. The shift has been gradual, but steady. This is good news for America, as a nation cannot survive if it cannot protect its most vulnerable (slippery slope paradigm).