Here is one take on her current (and potential future) stance on abortion and why Bush may pick her because of it.
Key parts from
http://balkin.blogspot.com/2005/07/edith-clement.html
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Known as a conservative and a strict constructionist in legal circles, Clement also has eased fears among abortion-rights advocates. She has stated that the Supreme Court "has clearly held that the right to privacy guaranteed by the Constitution includes the right to have an abortion" and that "the law is settled in that regard."
President Bush and his advisors have a litmus test for the next Supreme Court nominee.
But it's not the litmus test you are thinking of.
Liberals and Democrats alike are worried that the President will nominate someone who will vote to overturn Roe v. Wade. They needn't worry. That's not likely to happen. In fact, the only litmus test the President is likely to employ is whether a candidate promises *not* to overturn Roe. Here's why.
Bush must decide if he wants to overturn Roe or preserve the Republicans as the majority party. With Roe gone, the pro-choice movement will be energized and Republican politicians will have to state on the record whether they want to criminalize abortion. Women, libertarians, and moderates may bolt the party, destroying Bush's winning coalition. Republicans may dislike Roe, but they may dislike losing elections even more.
A far more prudent strategy, and the one the President and his advisors will likely adopt, would be to appoint Justices who will preserve Roe but chip away at it slowly, for example, by devising new procedural rules that make it difficult to challenge abortion regulations in federal court, by upholding restrictions on particular medical procedures like partial birth abortion, and by further limiting abortions for minors and poor women.
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(he continues with more at the link about)