But the spotlight is also filled with political perils for Mr. Graham. His previous comments, circulated widely in the hours after the announcement of Justice Ginsburg’s death, have injected a shot of energy — and cash — into the campaign of Mr. Harrison, who had already raised enormous sums and outspent Mr. Graham.

Under the quick timetable envisioned by Mr. Trump, who on Monday said he would prefer a confirmation vote before the Nov. 3 election, Mr. Graham would most likely be stuck in Washington in the run-up to the election, keeping him away from the campaign trail at a critical time.

For now, his critics are seeking to increase the pressure on Mr. Graham. The Lincoln Project, a group of Republicans dedicated to defeating Mr. Trump and his allies in the Senate, has teamed with an anti-Graham political action committee to turn footage of his 2018 remarks into a television advertisement culminating with the phrase: “Hold him accountable.” A spokesman for the Lincoln Project said the group was spending $750,000 to run the ad nationally beginning Tuesday.