President Trump on Tuesday accused Democrats of playing a "con game" with their calls for delays and investigations over sexual misconduct claims against Supreme Court nominee Brett Kavanaugh -- and cast doubt on one of the accusers, saying she "has nothing."

"It’s horrible what the Democrats have done, it’s a con game they’re playing, they’re really con artists," Trump told reporters at the United Nations, taking an increasingly aggressive stance in response to the ever-changing controversy.

“They’re good at one thing, it’s obstruction, and resisting and con,” he said.

Kavanaugh has been accused publicly by two women of sexual misconduct in high school and college. Democrats have seized on both accusations as reason to delay the confirmation vote for more hearings and a full FBI investigation.

Republicans have invited Christine Blasey Ford, who said Kavanaugh groped her at a party in high school 36 years ago, to testify on Thursday. Ford has accepted, but later raised concerns about the format of the hearing. Kavanaugh, who has repeatedly denied the claims, plans to testify Thursday as well.

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Meanwhile, the New Yorker magazine reported late Sunday that a Yale classmate of Kavanaugh claimed he exposed himself to her at a college party. Kavanaugh strongly denied that claim as a "smear." That account was quickly called into question, particularly as the magazine had not corroborated the account with witnesses and the acccuser -- Deborah Ramirez -- admitted that she doesn't fully remember the incident as she was drunk.

The magazine also reported that Ramirez spent six days "carefully assessing her memories and consulting with her attorney" before telling the full version of her story.

Trump on Tuesday expressed skepticism about Ramirez's account.

“The second accuser has nothing. The second accuser doesn't even know, she thinks maybe it could have been him, maybe not, she admits that she was drunk, she admits there were time-lapses," he said.

The remark took a different tone from the White House earlier in the day, when Press Secretary Sarah Sanders had said on ABC News that the White House "would be open" to having Ramirez testify.

Trump reserved most of his ire for the Democrats, whom he accused of playing a "very dangerous game" and hurting Kavanaugh's family.

"His wife is devastated, his children are devastated. I don't mean they're like 'Oh gee I'm a little unhappy,' they're devastated," he said. "It's just a game for [Democrats], but it's a very dangerous game for our country."

Kavanaugh on Monday went on Fox News accompanied by his wife, Ashley, to defend his name.

"What I know is the truth, and the truth is I've never sexually assaulted anyone," Kavanaugh told Fox News' Martha MacCallum in an exclusive interview.

Kavanaugh also told MacCallum that he would not withdraw his name from consideration over the allegations.

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"I want a fair process where I can defend my integrity, and I know I'm telling the truth," the judge said. "I know my lifelong record and I'm not going to let false accusations drive me out of this process. I have faith in God and I have faith in the fairness of the American people."

Republicans face a narrow path to confirmation for Kavanaugh, which could be derailed by a few defections from their own party.

Fox News’ Brooke Singman and Samuel Chamberlain contributed to this report.