Supreme Court nominee Sonia Sotomayor will begin making her rounds on Capitol Hill this week, meeting Tuesday with Senate Majority Leader Harry Reid (D-Nev.), Judiciary Chairman Patrick Leahy (D-Vt.) and Judiciary ranking member Jeff Sessions (R-Ala.).A meeting Tuesday with Senate Minority Leader Mitch McConnell (R-Ky.) also appears likely, according to White House Press Secretary Robert Gibbs.The White House is hopeful Sotomayor will stage several other courtesy calls with Senators next week, Gibbs said.Sotomayor will also complete and send to Senators next week a standard questionnaire provided to her by the Senate.