Beliefnet’s Steve Waldman asks the question on his blog.  He writes:

Some Democrats are now making an unusual argument about abortion: that a Democratic administration might actually reduce abortions more than a Republican administration?

On the surface, this seems preposterous. Republicans oppose abortion rights, Democrats support them. How could it possibly be that a Democratic approach would reduce abortion more?

It’s actually quite plausible under certain circumstances — though not, I must add, under the approach Barack Obama is currently taking.
Let me start with a basic point. If you look at abortion rates since Roe v. Wade you find something startling: during Democratic administrations (pro choice administrations) the average annual abortion rate is virtually identical to that under Republican administrations. Many factors help explain that but it does force us to conclude that there’s not a simple connection between whether you have a Republican president and lower abortion rates.