WASHINGTON — There is a reason Republican senators are so adamant in their refusal to let President Obama appoint a successor to Justice Antonin Scalia, a towering figure in conservative jurisprudence. An Obama appointment would be the most consequential ideological shift on the court since 1991, creating a liberal majority that would almost certainly reshape American law and American life.

“At-risk precedents run from campaign finance to commerce, from race to religion, and they include some signature Scalia projects, such as the Second Amendment,” said Lee Epstein, a law professor and political scientist at Washington University in St. Louis.

“Some would go quickly, like Citizens United, and some would go slower,” she said. “But they’ll go.”

Every time the party in the White House changes, there is a potential impact on the court as the new president tries to mold it when openings develop. But Mr. Obama has a relatively rare opportunity to make a third appointment at a crucial moment. “The court is now divided on many issues,” the president said on Tuesday. “This would be a deciding vote.”