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.
The President has little authority in creating laws, but can inform Congress on his views and in what direction he would like to see policy go. Many presidents choose not to address the abortion issue as people become very passionate about where they stand on this issue. Presidents also need the cooperation of Congress to have laws enacted and the two parties (democrats and republicans) have very different views on this subject. One way that a president can influence abortion law decisions is by appointed Supreme Court and federal judges when and if those positions become available. Presidents often appoint people to these positions who have similar opinions to them on issues such as abortion.