WASHINGTON, DC (CBSNewYork/AP) – President Donald Trump held fast to supporting Supreme Court nominee Brett Kavanaugh, saying the sexual misconduct allegations against his choice are “totally political.”

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Trump, at the United Nations in New York, declared that Kavanaugh is “outstanding,” and added, “I am with him all the way.”

He spoke as Kavanaugh’s nomination came under another cloud as The New Yorker published the account of a second woman who says he exposed himself to her while they were students at Yale. The woman said Kavanaugh forced her to come in contact with his penis while both were inebriated at a party.

The first accuser, Christine Blasey Ford, has said Kavanaugh assaulted her in high school. She says he covered her mouth and tried to remove her clothing. Ford and Kavanaugh are expected to testify on Thursday.

Kavanaugh has denied the allegations.

Earlier on Monday, White House counselor Kellyanne Conway said on “CBS This Morning” that the allegations against Kavanaugh are “starting to feel like a vast left-wing conspiracy.”

“I know there’s pent-up demand for women to get their day, women who have been sexually harassed and sexually assaulted, and I personally am very aggrieved for all of them, but we cannot put decades of pent-up demand for women to feel whole on one man’s shoulders. What exactly is the standard for ruining one man’s life based on decades of allegations that have nothing to do with him?” said Conway.

She added, “I just don’t think one man’s shoulders should bear decades of the MeToo movement.”

The New Yorker magazine reported Sunday night that Senate Democrats were investigating a second woman’s accusation of sexual misconduct by Kavanaugh dating to the 1983-84 academic year, Kavanaugh’s first at Yale University.

The New Yorker said 53-year-old Deborah Ramirez described the incident in an interview after being contacted by the magazine. Ramirez recalled that Kavanaugh exposed himself at a drunken dormitory party, thrust his penis in her face, and caused her to touch it without her consent as she pushed him away, the magazine reported.

In a statement provided by the White House, Kavanaugh said the event “did not happen” and that the allegation was “a smear, plain and simple.” A White House spokeswoman added in a second statement that the allegation was “designed to tear down a good man.”

The new information came hours after the Senate committee agreed to a date and time for a hearing after nearly a week of uncertainty over whether Ford would appear to tell her story.

Also on Monday, Michael Avenatti, the lawyer for Stormy Daniels, tweeted that he represents another woman “with credible information regarding judge kavanaugh.”

(© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)