This idiom or expression (which is not polite) means:

In trouble.
Under pressure.
In a messy situation that’s not easy to get out of.

A. Have you seen the test results?
B. Yes, I know, we’re deep sh-t!!

Also see:
In hot water.

This idiom or expression means:

Under (a lot of) pressure.

We are under the gun to get the play on the road by next week.

This idiom or expression means:

In trouble.
Under pressure.

Political scandals have landed several public figures in hot water.

Also see:
In deep sh-t. (Not a polite thing to say.)

This idiom or expression has to do with:

Changing one’s position or decision under pressure.

This idiom or expression is about:

Being faced with questions that one doesn’t want to answer.
Being held accountable for something that one has said or done.

Faced with questions about his personal indiscretions, the senator is finding himself in the hot seat.

This idiom or expression means:

Putting someone under pressure.
Forcing, or trying to force, someone to do something.

A. He’s not coming to my wedding.
B. I know him. You’ll have to hold his feet to the fire before he changes his mind.

Also:
Put someone’s feet to the fire.
Keep someone’s feet to the fire.