Gibbs said Sotomayor had meetings planned with Senate Majority Leader Harry Reid, Judiciary Committee Chair Patrick Leahy, and Jeff Sessions, the ranking Republican on the Judiciary Committee.
He also said there were efforts to set up a meeting with Minority Leader Mitch McConnell, and that "other visits can be scheduled for that Tuesday and throughout the remainder of the week."
CBS News Capitol Hill producer Jill Jackson reports that the meeting with Reid is presently scheduled for around 10:15 a.m. ET.
The closed-door meetings will give Sotomayor and the senators who will vote on her confirmation a chance to feel each other out before formal hearings begin.
Gibbs said the questionnaire Sotomayor is filling out for the Judiciary Committee "will go up to the Senate at some point next week." That document will include information on her finances and personal life as well as a discussion of specific rulings.