Some said a messy and unsuccessful filibuster fight would distract from the Democratic focus on other issues like corruption in government and wiretapping by the Bush administration.
The filibuster fight, like much of politics, is about power, a temptation from which not even moderates are immune.
Republicans said there were already signs that the filibuster fight was complicating the agenda.
In the meantime, Senate leaders, their advisers and outside interest groups are preparing for the filibuster fight.
If there is another filibuster fight in the Senate's future, it is at least a few weeks away.
Republican strategists consider the nominees - two women, one of whom is black - favorable choices for a filibuster fight.
And even some Democrats argue privately that a filibuster fight would not be worth it.
Republicans have indicated that Justice Owen of Texas could be the focus in the filibuster fight.
The emphasis Republicans placed on the legislative schedule marked a new front in the intense battle for public opinion in the filibuster fight.
The filibuster fight could re-emerge during a Supreme Court confirmation, and a big question is how Mr. Specter would handle it.