Senator Harry Reid, the majority leader, is prepared to move forward with a vote that could severely limit the minority party’s ability to filibuster presidential nominees, possibly as early as this week, Democrats said Tuesday.

Exasperated with the refusal of Senate Republicans to confirm many of President Obama’s nominees, Mr. Reid has been speaking individually with members of his caucus to gauge whether there is enough support to change filibuster rules. …

Mr. Reid, of Nevada, has picked up crucial support from some of his more reluctant members recently. Senator Patrick J. Leahy, Democrat of Vermont and the longest-serving member of the Senate today, who is chairman of the Judiciary Committee, has endorsed putting limits on the filibuster despite his history of being protective of Senate institutions.

The two senators from California, Dianne Feinstein and Barbara Boxer, said separately on Tuesday that they were leaning toward a rules change.