WASHINGTON — Trading accusations, Democratic and Republican senators quarreled Tuesday over who will testify at what promises to be a dramatic and emotional hearing next Monday with Supreme Court nominee Brett Kavanaugh and the woman who says he sexually assaulted her when they were in high school. But doubts were raised whether she would appear.

Kavanaugh was at the White House for a second straight day, but again did not meet with President Donald Trump. The president said he was “totally supporting” Kavanaugh and rejected calls for the FBI to investigate the accusation.

“I don’t think FBI really should be involved because they don’t want to be involved,” Trump said. As for Kavanaugh, he said, “I feel so badly for him that he’s going through this, to be honest with you. … This is not a man that deserves this.”

Democrats are demanding that the FBI be given time to reopen its background investigation into Kavanaugh so it can check the assertions of Christine Blasey Ford, the woman accusing Kavanaugh of assault. They say the hearing should not move forward until that investigation is completed.