Looming deadlines on 19 January 2024 and 2 February 2024 for different government functions could mark the first federal shutdown since December 2018 to January 2019 (Congressional Research Service, USA Today). For the purposes of this question, a "shutdown of the US federal government" would mean a ceasing of operations due to a lack of funding appropriation. A partial shutdown would count (Committee for a Responsible Federal Budget). As a reminder, this question is, by default, governed by dates in the Pacific Time Zone.

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NOTE 23 March 2024: While funding appropriation lapsed at midnight ET, the question description states that "a 'shutdown of the US federal government' would mean a ceasing of operations due to a lack of funding appropriation." Per the White House,

"[The Office of Management and Budget] has ceased shutdown preparations because there is a high degree of confidence that Congress will imminently pass the relevant appropriations and the President will sign the bill on Saturday...Because obligations of federal funds are incurred and tracked on a daily basis, agencies will not shut down and may continue their normal operations." (emphasis added)

Therefore, since there was no "ceasing of operations," the question will remain open.