It will certainly depend on your gates. I had a 35 min connection with my family two weeks ago, and the flight was running a bit late. It worried us, but we made up some of our departure delay in the air (i.e., the schedule was padded). We parked with a little under 30 minutes to departure time. We quickly deplaned, starting looking for our gate - and it was across the hall. We arrived just as our zone (2) was being called.

On the other hand, our outbound at O'Hare required a terminal change, and we needed a good 20 minutes just to make the walk.

As long as you're on the same airline, and not doing regional/express to mainline or something similar, you will be at the borderline of OK if everything is exactly on time.