Story highlights Michael Smerconish spoke with Spicer shortly before he quit as press secretary

CNN host says Spicer gave no indication he was leaving the White House

(CNN) Michael Smerconish scored what he called Sean Spicer's "exit interview" as White House press secretary, though he didn't realize it at the time, the CNN host said Saturday.

Smerconish was in Washington on Friday to interview Arnold Schwarzenegger as well as to have an off-the-record chat with Spicer. The two met at 9 a.m., and Smerconish left 45 minutes later.

"I didn't want to overstay my welcome -- he'd told me he was meeting with the President at 10," Smerconish said.

"By the time I'd returned to my hotel and turned on the television, word was breaking that he'd just quit as White House press secretary ," he said.

Following a rocky six months on the job, Spicer resigned after President Donald Trump named Anthony Scaramucci, a New York financier and former Trump campaign fund-raiser, as the White House communications director. At a press conference later Friday, Scaramucci announced that Sarah Huckabee Sanders, the principal deputy press secretary, would replace Spicer.

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