Tom McClusky, a vice president at the anti-abortion organization Family Research Council, said of Sotomayor, "She will, I'm sure, find reasons not to answer those questions. So until a case comes up before the court, which could happen relatively soon, we won't know how she will rule."
Obama recently stepped into the abortion controversy when Notre Dame invited him to speak despite opposition from anti-abortion protestors.
There he said, "The fact is that at some level, the views of the two camps are irreconcilable. Each side will continue to make its case to the public with passion and conviction."
Some anti-abortion groups tried to stop the confirmation of Obama's choice for secretary of Health and Human Services, former Kansas Gov. Kathleen Sebelius, who supports abortion rights.Critics noted she had accepted campaign donations from Tiller.
Hours after Tiller's murder, an anti-abortion leader warned Obama and other Democrats not to use the murder to build support for abortion rights. The Rev. Pat Mahoney of the Christian Defense League said, "Do not take this personal tragedy and try to use it for political gain."
Sunday evening, the White House issued a statement from the president, who said he was shocked and outraged by the murder.
"However profound our differences as Americans over difficult issues such as abortion, they cannot be resolved by heinous acts of violence," Obama said.
As for Sotomayor, the White House has said that the president has not questioned her about abortion. But it also said he is very comfortable with her interpretation of the Constitution.
ABC News' Lauren Sher contributed to this report.