I've never had the meltdown but can understand it. In my case I got off the flight 7 minutes before my next flight. I know to short, well it was because of a 2 hr. delay so I had almost 2hrs and 10 minutes originally. I only had to go over 2 gates and got there with over 5 minutes. Door was closed and plane had been pushed back and GA was gone.
The interesting part was I new 2 friends that had left earlier in the day after taking 2 bumps that day to see were they where. They were in my seats, the plane it was over sold and they loaded and pushed away 10 minutes before departure time full. Another 4 people showed up soon after also looking for the flight. We all ended up spending the night in MSP. Nice Hotel and Breakfast but that was it.