But at least one political scientist said Friday it was a long shot.
"Lightning would have to strike," for her to be appointed, said College of Charleston professor David Mann, who follows the Supreme Court and judiciary closely.
Williams, the daughter-in-law of former state Sen. Marshall Williams, was appointed to the federal bench in 1992 by President Bush's father.
She was the first female on the 4th Circuit, which many consider the most conservative court in the federal appellate system.
South Carolina Chief Justice Jean Toal said Williams would fit President Bush's conservative ideology and she is lawyer with considerable trial experience.
"Isn't that a wonderful suggestion?" Toal said when she heard Williams' name had been mentioned.
Williams wrote an opinion setting the stage for an overruling of Miranda, a due-process opinion only conservative justices Clarence Thomas and Antonin Scalia voted to affirm.
---
Information from: The State, http://www.thestate.com/