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1.
Not having the time to take a shit all day even though you know you have to. Or if there is not a place to take a shit.

When you are on a first date and you know you can't excuse yourself to take the kids to the pool.

When you are riding with your boss all day and know you can't ask your boss to pull over so you can have a shit.

On your first day at the new office when you can't ask the receptionist or your new boss where the bathroom is only to be gone for 20 minutes dropping the bomb.
I was up against two deadlines and had meetings throughout the day - I had to drop a deuce but I knew I would be pinching a no shitter which made me sweat and my guts quiver.
by Deuce Bigelow February 04, 2014
 
2.
To go all day without taking a shit, in reference to baseball's "pitching a no hitter".
John was so busy at work today, he was pinching a no-shitter.
by jhook May 16, 2012