As an undergraduate at Dartmouth College, where he was a writer and the editor in chief of The Dartmouth Review, Mr. Menashi criticized women’s marches against sexual assault, arguing they discriminated broadly against men. He compared the gathering of race data by colleges to Nazi Germany’s Nuremberg laws; called animal-rights activists “by and large, a contemptible bunch”; and defended a fraternity’s themed “ghetto party,” to which a white student had worn an Afro, calling it “harmless and ultimately unimportant.”

As an editorial board member for the New York Sun newspaper, Mr. Menashi helped write a piece praising Christian students for persuading their university to allow a religious group on campus to bar gay people from becoming officers. In a 1998 Op-Ed for The New York Times, he argued against need-based financial aid at educational institutions, saying it “punishes families with the foresight and prudence to save.” In a book review in 2002, he advanced the myth that John J. Pershing, an American general in World War I, had executed Muslim prisoners using bullets dipped in pig fat. And in a 2010 law review article that has drawn particular attention, Mr. Menashi defended ethnic homogeneity in the context of Israel.

Mr. Menashi, who submitted more than 900 pages of supplementary material to the Senate Judiciary Committee, has expressed regret “if some of the writing was overheated or extreme,” and he has sought to draw a distinction between his thinking before and after law school. He graduated from Stanford’s law school in 2008.

The White House did not respond to a request for comment Wednesday about either nominee.

At a nomination hearing last month, Mr. Menashi said that the religious persecution his Jewish family had faced had helped shape his views. “My family illustrates the need and importance of America’s tradition of religious tolerance and diversity,” he said. “I abhor discrimination.”

Some of Mr. Menashi’s detractors have pointed to the legacy of the seat he would fill, which once belonged to Thurgood Marshall, the first black justice on the Supreme Court and a pillar of the civil rights movement. They have also pointed to the centrality of the Second Circuit to a number of legal matters concerning the president himself. The court has considered President Trump’s potential immunity from criminal investigation while in office and whether the president can block people from following his Twitter account without violating the First Amendment.

Mr. Menashi’s nomination has moved at an especially fast pace, having been made only last month. He is the second lawyer working in the White House Counsel’s Office to be nominated; Greg Katsas, former deputy counsel and deputy assistant to the president, was confirmed to the federal appeals court in Washington, D.C., in late 2017.

Democrats and Republicans pressed Mr. Menashi at a hearing last month to be more forthright about his work for the Trump administration. Senator Lindsey Graham, the Republican chairman of the Judiciary Committee, and Senator John Kennedy, Republican of Louisiana, called on him to answer yes-or-no questions, which he declined to do, citing lawyer-client privilege.