(CNN) President Donald Trump's incoming acting chief of staff Mick Mulvaney said the partial government shutdown could continue into next year.

"It is very possible that the shutdown will go beyond the 28th and into the new Congress," Mulvaney said on "Fox News Sunday" as the shutdown began its second day.

After Trump and Congress failed to resolve a dispute over funding for border security and Trump's border wall on Friday, the government went into partial shutdown. Mulvaney said Sunday morning that the White House had moved down from its demand for $5 billion and hoped Democrats would move up from their offer for $1.3 billion in border security funding.

Mulvaney's comments came after the Senate adjourned on Saturday, which meant the shutdown would likely continue past Christmas.

In an interview on ABC's "This Week," Mulvaney said Trump remained steadfast in his demand for wall funding.

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