They doubt his declaration that he was unaware that Democratic strategy documents he was given on judicial fights had been pilfered from Democratic computers by Republican staff between 2001 and 2003. Despite his repeated denials, they believe that he played a role in developing Bush administration policy on the treatment of terrorism detainees and that he prepared certain conservative judicial nominees for their hearings. They say new documents disclosed for his Supreme Court confirmation scrutiny show that he lied when questioned on those topics in confirmation hearings for his seat on the United States Court of Appeals for the District of Columbia Circuit. That court, of course, is known as the steppingstone to the Supreme Court.

“Judge Kavanaugh’s testimony had real issues of credibility,” Senator Chuck Schumer of New York, the Democratic leader, said Monday on the Senate floor, asserting that the nominee’s issues extended far beyond the sexual assault allegations to his White House work. “Is Judge Kavanaugh the kind of upright, straightforward individual we want on the bench?”

Even Judge Kavanaugh’s once prestigious clerkship — the sort of appeals court posting avidly sought by all ambitious Ivy League law school graduates — has become problematic. Before a Supreme Court stint with Justice Anthony M. Kennedy, Judge Kavanaugh clerked for Alex Kozinski, a veteran federal appeals court judge in California who stepped down after charges of sexual misconduct and maltreatment of employees. Judge Kavanaugh faced questions about his awareness of his mentor’s objectionable behavior. He said he saw no such conduct.

Despite the president’s embrace of Judge Kavanaugh, he was not on Mr. Trump’s initial list of Supreme Court prospects issued during the 2016 presidential campaign that he and his advisers compiled with conservative judicial allies from the Heritage Foundation and the Federalist Society. In keeping with Mr. Trump’s outsider image, many of those judges were serving on appeals courts outside Washington and others were on state courts.

Judge Kavanaugh, known to be a favorite in Washington legal circles and someone highly regarded by Donald F. McGahn II, the White House counsel, was one of five candidates added to list in November 2017, making him eligible for a Supreme Court nomination since the president had promised to choose only from those on his list.