New York Mayor Michael Bloomberg wished Jake Tapper “good luck with your show” yesterday while appearing on the debut episode of The Lead With Jake Tapper. The new one-hour CNN show looks like it needs it: The premiere of the first new show under new boss Jeff Zucker drew 400,000 total viewers, finishing in third place among cable news shows in its 4 PM ET time slot. That’s less than half of the 1.102 million who watched Fox News Channel’s Your World With Neil Cavuto, and also down from the 479,000 who watched Martin Bashir’s daily show on MSNBC. In the key adults 25-54 demo, the show starring the former ABC News White House correspondent — who new boss Zucker has called the “face of the new CNN,” — drew 87,000 viewers compared to Cavuto’s 172,000 and Bashir’s 100,000. It also was beaten it in the slot by CNN sister station Headline News, which pulled in 779,000 total viewers and 21,000 in the new demo.

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The Lead was also down sharply from what The Situation Room was getting in the time slot last week. The Wolf Blitzer-hosted show drew 427,000 viewers on March 11. It did, however, gain significantly from the 54,000 in the 25-54 demo compared with Situation Room‘s 4-5 PM hour.

Kicking off with an interview with Bloomberg, the show had “that new set smell,” as Tapper said in his opening minutes. Segments on Hilary Clinton coming out for gay marriage, mammograms, Robert Mugabe and an interview with Comedy Central’s Stephen Colbert on his sister’s Congressional run in South Carolina filled out the breezy show by the former ABC White House correspondent. Tapper, who also serves as CNN’s Chief Washington Correspondent, joined the news network on December 20, 2012.