By early afternoon, eight senior officials had disavowed the piece, including Vice-President Mike Pence, Secretary of State Mike Pompeo and Defence Secretary James Mattis, while hammering the author for writing it and the Times for publishing it. His deputy chief of staff said Pence's office is "above such amateur acts".
Ms Nielsen, along with Mr Pence and director of national intelligence Dan Coats were among the favourites on Thursday among political gamblers taking an online stab at guessing the author.
The Times said the writer is a senior administration official whose job would be at risk if the person's identity were to be made public.
"I would know. I am one of them". Some who agreed with the writer's points suggested the president's reaction actually confirmed the author's concerns.
He also says the timing of the op-ed's publication shouldn't be lost and encourages the President to stay focused on the midterm elections.
On Wednesday evening, before demanding that the Times unmask the writer, Trump tweeted one word: "TREASON?"
Senior staff in key U.S. national security and economic policy roles charged the article's writer with cowardice, disloyalty and acting against America's interests in harsh terms that mimicked the president's own words. That's a rich criticism coming from an administration that, like its predecessors, routinely holds briefings and phone calls with reporters that require the reporters not to identify the administration officials involved by name.
Whether the New York Times should have published an anonymous op-ed is an interesting question. That measure defines methods to legally remove a president from office. "But no one wanted to precipitate a constitutional crisis", the op-ed says.
President Donald Trump on Friday slammed investigative journalist Bob Woodward's damning portrayal of the inner workings of the USA president's administration as a "scam", alleging that it includes made-up quotes.
Sanders also urged the Times to issue an apology.
There is a quiet resistance within the administration of people choosing to put country first.
He called the White House a "well-oiled machine".
Trump lashed out at the author of the anonymous piece - and at the "dishonest" Times. The book is set for release next Tuesday.
The piece compared Trump unfavorably to the late Sen.
Steve Herman reported this story for VOA News.