Definition of keep cool with Coolidge?

Answer 1

This was the campaign slogan used by Calvin Coolidge during his successful presidential campaign in 1924. The president and the press continued to use it, referring to Coolidge's steady but laid-back leadership style.

Answer 2

This was obviously a campaign slogan for Calvin Coolidge, It was often printed on paper fans .

I doubt that Coolidge said it very often.

Perhaps some other president said it sarcastically, but I do not know that any did.