push the panic button, to

push the panic button

To overreact to a negative situation with an inordinate amount of fear, alarm, or confusion. If you're going to be a successful boss, you can't push the panic button every time your company has a minor setback. New parents tend to push the panic button over every little sniffle their first baby gets. You learn to chill out when you have more kids.
See also: button, panic, push
Farlex Dictionary of Idioms.

push the panic button

Also, press the panic button. Overreact to a situation, as in Don't worry; Jane is always pushing the panic button, but I'm sure the baby's fine. This term originated during World War II, when certain bombers had a bell-warning system so that the crew could bail out if the plane was severely hit. Occasionally a pilot would push the button in error, when there was only minor damage, causing the crew to bail out unnecessarily. By 1950 the expression had been transferred to other kinds of overreaction.
See also: button, panic, push
The American Heritage® Dictionary of Idioms by Christine Ammer.

push the panic button

verb
See hit the panic button
See also: button, panic, push
McGraw-Hill's Dictionary of American Slang and Colloquial Expressions

push the panic button, to

To overreact to a supposed emergency. This term originated during World War II, when B-17 and B-24 bombers had a bell-warning system so that the crew could bail out when the plane was badly hit. Occasionally this button would be pushed by mistake and the crew would bail out unnecessarily, even though the plane was virtually undamaged. By extension, the term came to mean acting in needless haste. In the 1950s it gained currency—and a more sinister meaning—when it also referred to releasing a nuclear warhead by pushing a button.
See also: panic, push
The Dictionary of Clichés by Christine Ammer
See also:
  • push the panic button
  • press the panic button
  • press/push the panic button
  • hit the panic button
  • fall all over
  • fall all over (one)
  • make a fuss of/over somebody/something
  • make a fuss over (someone or something)
  • make a fuss of (someone or something)
  • fuss over