Democrats insisted they could use the court fight to spur voters on the individual priorities that resonate with them, citing the stakes for climate change, campaign finance changes, abortion rights, immigration — mobilizing them on a topic that goes beyond the court but is tied to who chooses the new justice.

Whoever turns out to be right, both sides hardened their positions on Thursday as one potential nominee, Brian E. Sandoval, Nevada’s Republican governor, sent out a statement that he did not wish to be considered for the job.

Democrats opened their assault when more than two dozen senators stood in a brisk wind in front of the Supreme Court and criticized Republicans for what they said was outrageous intransigence in refusing to consider any nominee to fill the spot left by the death of Justice Antonin Scalia.

“We have obstruction that is on steroids,” said Senator Harry Reid of Nevada, the Democratic leader. “Never in the history of the country has there been anything like this.”

But while the tableau of United States senators standing before the court’s iconic marble pillars underscored the Democrats’ determination to raise public pressure on Republicans, it also accentuated their powerlessness, in terms of legislative procedure, to force action on a nominee.

Republicans adopted a strategy of trying to deflect attention from the court fight and move on to other business in the Senate.

“I think our friends across the aisle would agree that there is a lot of important work that we can, and should, do together,” Senator John Cornyn of Texas, the No. 2 Senate Republican, said in a floor speech urging everyone to get back to work. “I would ask our friends across the aisle, while they come out on the floor or give news conferences and express mock horror, to tone down the rhetoric and avoid the hypocrisy that seems so apparent when they argue for different standards today than they advocated in the past.”