1) Both agree that abortion is moral tragedy for all of the people directly involved and for society as a whole.
2) Many (perhaps not all, but the bulk) agree (either explicitly or tacitly) that the criminal law is too blunt to be the principal instrument for regulation of this complex social problem.
3) When considering various regulatory paths, many (again, perhaps not all, but the bulk) agree that practical solutions should weigh very heavily the host of public health problems that would arise if abortion is driven underground.
I won't say that I wholeheartedly endorse these principles, but they do have some appeal to me, and strike me as a point where persons of all persuasions on the issue of abortion can try and unite over common ground.
See also the Democrats' 95-10 plan on abortion. The plan seeks to reduce the abortion rate in the U.S. by 95% over the next 10 years through a variety of mechanisms, like increased access to contraception, increased healthcare options for young women, better sex ed programs, tax credits for adoptions, and child-care services for mothers in college. It has support from both pro-life and pro-choice Democrats, because it demonstrates a just and humane solution to a difficult social problems.
Even pro-choice Democrats don't cheer the act of abortion. We cheer access to the procedure, to be sure. We think that the availability of abortion is important to granting women a equal position in the American polity. But no women gets excited and flush-faced at the prospect of abortion. Nobody throws a party for an intrusive medical procedure. Reducing the number of abortions doesn't stand in opposition to a pro-choice sentiment, as long as the methodologies we use in the effort fundamentally respect a woman's equal status and are cognizant of her health, welfare, security, and freedom. The more the Democrats can push that message, the better off they'll be.