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Press secretary Sarah Sanders is scheduled to brief reporters at the White House on Thursday.
It will be Sanders' first opportunity to field questions from the media after the Trump administration made multiple high-level staff changes.
On Wednesday, the White House confirmed Larry Kudlow will be the next director of President Donald Trump's National Economic Council.
Kudlow, an economist and longtime CNBC pundit, was an informal advisor to Trump during the campaign. He replaces Gary Cohn, who resigned shortly after Trump announced broad tariffs on imports of steel and aluminum in early March.
Tillerson had been a target of Trump's ire for much of his tenure. In July, Tillerson reportedly called Trump a "moron" after a meeting; in October, Trump admonished Tillerson on Twitter for "wasting his time" trying to negotiate with North Korea on nuclear weapons.
News reports also revealed on Tuesday that Trump's personal assistant, John McEntee, was fired and escorted from the White House this week. McEntee is reportedly under investigation by the Secret Service for financial crimes.
Meanwhile, Democratic congressional hopeful Conor Lamb was projected the apparent winner of a Pennsylvania special election in a district Trump won by 20 points during the 2016 presidential race. Many pundits consider the upset to be a warning sign for Republicans in the upcoming midterm elections, though some GOP leaders have downplayed the implications of Tuesday's outcome.