WASHINGTON — The two Republican senators sat together on one couch, while the Democratic senators sat a few feet away on another, but the gap between them in Tuesday’s meeting with President Obama in the Oval Office could hardly have been bigger.

After the discussions about choosing a nominee for the Supreme Court seat left vacant when Justice Antonin Scalia died, Senate Minority Leader Harry Reid of Nevada and Senator Patrick Leahy of Vermont emerged and quickly denounced their Republican colleagues before a bank of TV cameras set up outside the West Wing of the White House.

“They think they are going to wait and see what President Trump will do, I guess, as far as the nomination is concerned,” Mr. Reid said, referring to Donald J. Trump, the Republican presidential front-runner.

Mr. Reid said the meeting was brief. “We killed a lot of time talking about basketball and other stuff,” he said. Mr. Reid described the Republicans as implacable and said there was nothing to suggest that they might budge.