WASHINGTON — 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.

Given how much deference senators have traditionally shown to the rules and procedures of the institution — many of them in place since the 18th century — any modifications are a serious undertaking.

But among Democrats there is a strong consensus that Republicans have gone too far in their latest attempt to block White House appointments, by denying Mr. Obama any more judges for what is considered the most important appeals court in the country despite three vacancies.