Fill in the blank with the most appropriate phrase.

To prepare the exhibition hall before the delegates arrived, the organizers worked ______ to finish setting up the displays.

The correct option is around the clock.

Explanation:
The context of the sentence refers to the organizers making continuous, intense effort to complete the setup of the exhibition hall before the delegates arrive.

Let's analyze the meanings of the provided idioms:

1. around the clock: Working continuously all day and night without stopping.
2. at the drop of a hat: Doing something immediately or without any hesitation.
3. out of the blue: Happening completely unexpectedly or without warning.
4. under the weather: Feeling slightly unwell or sick.

Therefore, the idiom around the clock fits logically and grammatically into the blank to show that they worked non-stop to finish the preparations on time.