The timing has meant that the attention of Democrats has been divided as they devoted substantial time and resources to failed attempts to derail Trump cabinet nominees. They have also been occupied battling the new administration on multiple other fronts such as the repeal of the health care law, the president’s executive order on immigration and demands for an independent inquiry into Russian meddling in the 2016 election.

At the same time, Democrats have emerged from one-on-one meetings with Mr. Gorsuch praising his intellect and demeanor, though some have said he failed to provide persuasive answers on basic constitutional issues.

The situation was worrying enough to Gorsuch opponents on the left to provoke a chastising letter to Senate Democrats. “Democrats have failed to demonstrate a strong, unified resistance to this nominee despite the fact that he is an ultraconservative jurist who will undermine our basic freedoms and threaten the independence of the federal judiciary,” the 11 groups wrote. “We need you to do better.”

The letter also followed a sense among progressives that Democratic members of the Judiciary Committee who will consider the Gorsuch nomination had not been aggressive enough in their treatment of Jeff Sessions, their former Republican colleague, during his confirmation hearing for attorney general — a hearing some viewed as a test run for a Supreme Court fight.

Senator Jeff Merkley, the Oregon Democrat who joined Ms. Murray at Tuesday’s news conference, said the progressive groups were right to try to stir him and his colleagues to action.

“I think they are doing exactly what they should be doing,” he said. “We have to pivot and really focus on this Supreme Court nomination.”

Other Democrats say Judge Gorsuch will struggle to win the eight Democratic votes he would require to be assured of overcoming a filibuster. They believe the hearing will stiffen the party resolve, particularly if he is not more forthcoming with answers about how he views the role of an independent judiciary in standing against the presidency.