The president wants Elena Kagan, who is the U.S. solicitor general, confirmed and seated on the top court when it reconvenes in October.
If Republicans do not filibuster, the 59-member Senate Democratic Caucus is considered virtually certain to confirm her, regardless of how the 41 Republican senators vote.
Kagan received more good news Sunday when former first lady Laura Bush called for more women in politics and government and praised Kagan's nomination.
"I think it's great. I'm really glad that there will be three, if she's confirmed. I like to have women on the Supreme Court," Mrs. Bush said.
If confirmed, Kagan will join Ruth Bader-Ginsburg and Sonia Sotomayor to give the court three female justices for the first time.