Sonia Sotomayor will meet with 10 senators -- the Senate leadership and several members of the Judiciary Committee -- on Tuesday.

The Supreme Court nominee will visit with Majority Leader Harry Reid, D-Nev.; Minority Leader Mitch McConnell, R-Ky.; Majority Whip Richard Durbin, D-Ill.; Minority Whip Jon Kyl, R-Ariz.; Judiciary Chairman Patrick Leahy, D-Vt.; Judiciary ranking member Jeff Sessions, R-Ala.; and Sens. Charles Schumer, D-N.Y., Orrin Hatch, R-Utah, Dianne Feinstein, D-Calif., and Kirsten Gillibrand, D-N.Y.

Rachel Brand, who helped the Bush White House prepare John Roberts and Samuel Alito for their Supreme Court confirmations, said the substance of these "courtesy" meetings is almost entirely up to the senator. "These meetings tend to be highly idiosyncratic.... If you know something about the senator, you could guess what [the meeting] is going to be about. It's impossible to generalize."

But they're crucial nonetheless, she said.

"It's a really important part of the process," Brand said. "Both in terms of shaping the senators' views of the nominee and also for the administration to get a feel for what kinds of things the senators are concerned about."