Story highlights Gary Cohn is the director of the National Economic Council and a high-profile Jewish member of the White House

In an interview, he said the Trump administration "can and must do better" condemning hate groups

(CNN) Gary Cohn, the National Economic Council director, was on the brink of resigning after President Donald Trump's freewheeling press conference earlier this month in which he likened white supremacists to counter-protesters in Charlottesville, Virginia.

The moment laid bare uneasy rifts in the White House between Trump's nationalist backers -- including Steve Bannon, who was forced out days later -- and more liberal advisers such as Cohn.

However, a number of embattled administration officials have toyed with the idea of departing the administration amid the chaotic first months of the Trump presidency. Often, they find a compelling reason to stay.

In Cohn's case, people familiar with the situation say he's made no secret of the fact that he's vying to become the next chairman of the Federal Reserve. The potential to land such a prominent position might have been a factor in his decision to stay, they say.

Another source close to Cohn cautioned that while Cohn was very upset, he didn't seriously consider resigning.

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