Spokeswoman Sarah Huckabee Sanders said they will determine what to do "as the day goes on and as we see how the next couple of hours go."
Treasury Secretary Stephen Mnuchin is leading a delegation of Cabinet members and top aides to the glitzy summit in the Swiss Alps. He was scheduled to leave today, with President Donald Trump following later in the week.
Trump planned to bring his "America First" message to the conference, a gathering of global political and business elites which has rarely been attended by recent sitting presidents.
One member of the delegation, FDA Commissioner Scott Gottlieb, stressed on Twitter Monday that he was not traveling. He said on Twitter: "I'm in White Oak, MD today at #FDA headquarters. I did not travel to Davos today as previously planned."
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Secretary of State Rex Tillerson won't travel to Davos if the government is still shut down, said Undersecretary of State Steve Goldstein, adding that the decision would likely be made Wednesday. In that case, Tillerson, who is traveling in Europe, would return to Washington, meaning he would also cancel a planned post-Davos stop in Warsaw, Poland.
He added that "if this continues to drag on it will become more difficult to find more ways for the president to get there too.
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