The vote on the resolution passed the Democrat-led panel on a 24-17 party line vote following an occasionally heated markup hearing.
Cohen says he was offered a job "working with Don McGahn at the White House general counsel's office" but turned it down.
"I was happy to voluntarily sit down with them," Sanders told CNBC.
The president's decision follows a week of speculation about who would succeed Kelly. The retired general is set to leave by year's end.
The president's about-face toward Woodward, in spite of his history of compliments for the reporter, provides another stark example of Trump's scorched-earth tactic of responding to his critics.
White House chief of staff John Kelly issued a statement denying that "I ever called the President an idiot."
President Donald Trump's attorney says that if the claims in Bob Woodward's book are true, it is time for some members of the administration to resign.
Trump's lawyers see Flood as a critical piece in their strategy to combating any attempt by Mueller at issuing a subpoena for the president to appear before a grand jury, a person close to the president's legal team told CNBC.
White House counsel Don McGahn will oversee President Donald Trump's selection of a nominee, and the overall confirmation process.
Trump asked Attorney General Jeff Sessions to reverse his decision to recuse himself from the investigation into Russian efforts to influence the 2016 election, The New York Times reported.
One year ago, Robert Mueller was appointed as special counsel to take over the Justice Department's investigation into possible coordination between Russia and Donald Trump's 2016 presidential campaign.
The comedian delivered a profanity-lace diatribe that sharply departed from the traditional spirit of the evening.
The president is always in charge at the White House, but the chief of staff is usually known as the one who keeps everything in order. That has changed in President Donald Trump's administration.
Former Vice President Joe Biden could be a "pretty serious" candidate to challenge Donald Trump in the 2020 presidential race, Reince Priebus said Wednesday.
"I don't know if their folks are bragging that they were doing things that they weren't. Maybe they were doing things, I don't know," he said of Cambridge Analytica.
Speaking with CNBC Wednesday in Hong Kong, former White House Chief of Staff Reince Priebus said the Trump administration's tough trade talk is not populism or nationalism — it's "Trumpism."
Constitutional watchdogs and former government officials criticized the reported use of NDAs in the White House.
Trump has parted with more top-level staff in his first year than any of his five most recent predecessors did in their respective first years.
Democratic members of the U.S. House of Representatives Intelligence Committee said they will put out their own report that will "set out for the country what evidence we have seen to date."
Trump asked former Chief of Staff how the investigators had treated him, the New York Times reported.