“In this Week 1 and Week 2,” he vowed, “you’re going to see shock and awe.” The Judicial Crisis Network has said it will spend $10 million on a campaign to support Mr. Gorsuch.

In a demonstration of how closely Mr. Trump plans to rely on the coalition, he gathered several of its leaders at the White House on Wednesday, including the N.R.A. president, Wayne LaPierre; the antitax activist Grover Norquist; and Marjorie Dannenfelser, who heads the Susan B. Anthony List, a group that opposes abortion. The scene, in the Roosevelt Room, was a vivid reminder of how the changeover in Washington has opened the White House door to conservative movement players who found themselves shut out for the last eight years.

The breadth of their effort underscores what the movement considers to be at stake. Business regulations, abortion restrictions, religious expression and voting rights could all be before the court in the coming years.

The mobilization now underway illustrates the unique power that the Supreme Court has in energizing the right. Exit polls showed that 21 percent of voters said the court was the most important factor in their decision. Mr. Trump overwhelmingly carried them, 57 percent to Hillary Clinton’s 40 percent.

In an attempt to placate skeptical conservatives during his campaign, he took the unprecedented step of providing movement leaders with the list of names from which he would pick, leaving activists reasonably assured that they would be comfortable with his decision. They felt that assurance because many of them — including those now working on the Gorsuch confirmation campaign — suggested the names in the first place.

“He was smart enough to understand that he needed to make that promise, and in a highly tangible and credible way,” said Ralph Reed, founder of the Faith and Freedom Coalition and one of the conservative leaders Mr. Trump invited to the White House on Tuesday to watch the Gorsuch announcement. “That was, of course, because of the deep paranoia on the right that he would betray them.”