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At an all-senators meeting Monday morning, Republicans hope they can talk the majority out of pressing ahead.

Ahead of the showdown, each side deployed numbers to argue its case.

Republicans said they have confirmed an exceptional number of Mr. Obama’s nominees, including every executive branch appointment that has come to the Senate floor. They say they have obstructed only a few judges who were outside of mainstream legal thought.

Democrats say Republicans have pushed obstruction behind closed doors by slow-walking nominees in committees, demanding answers to hundreds of questions about their histories and policy positions.

Mr. Reid said Republicans usually don’t even object to the nominees, but rather are using them to attack the president’s policies or the role of government itself.

“They have nothing against the qualifications. They don’t like the jobs these people have,” Mr. Reid said.

The filibuster is not part of Senate rules. It’s a term that is applied when a single senator or group of senators wants to hold an indefinite debate on an issue.

Some issues and motions, such as bringing a budget to the Senate floor, are considered nondebatable and cannot be filibustered, but most of the regular motions are debatable. It takes 60 votes to cut off debate. When that vote fails, it is considered a filibuster.