On the weekends, the office is generally staffed with just a few people, who answer the phones, monitor the weather, issue forecasts for pilots and post regular updates on social media.

Then the president weighed in with his weather update.

“It just started this big blitz,” said Mr. Garrison, an employee since 2002. “We were just caught in the crossfire.”

Some in the office have felt bewildered.

Chris Darden, the office’s meteorologist-in-charge, posted to his personal Facebook account that the past days had been the “most confusing and disheartening” of his career.

One meteorologist in the Birmingham office tweeted that he was “crawling out from under this bus” on the day NOAA issued the unsigned statement that many forecasters saw as a challenge to the Weather Service.