What specific role or action does the President have in affecting abortion laws?

The President might not be able to directly change or
amend the case law on the issue of abortion.  However, the President can help to
initiate a public discussion of the issue of abortion.  In doing this, the President can
impact how public view of the abortion issue can influence lawmakers on both local and
national levels to make laws and policies that can either make abortion easier or more
difficult.  Issues such as parental consent, public funding of abortion clinics, and
even sanctions against those who commit crimes against those who perform abortions are
all ways in which the President and other lawmakers can influence the abortion debate. 
The President might not be able to pass a law that bans or completely permits abortions,
but the President is able to strongly sway the debate with their own stance and
influencing policies and laws towards that end.  The idea of the President holding their
own opinions about the issue of abortion can also provide a sense of subtle impact in
the President affecting abortion laws.