Had the exact same thing happen a couple years ago as well. There were quite a few pilots deadheading on the flight and I first knew something was up when the FAs were walking around asking if any of them were 57 qualified. Then they made the announcement, "We are delayed for a couple reasons...the inbound flight was a few minutes late, and maintenance has a small repair they needed to make...but mostly our pilot is stuck in traffic!" Delta was really good about assuring us they would take care of us if we missed our connections with hotels and compensation. Finally got into SLC, and I had already given up hope on making my connection since we arrived 15 minutes after my connection was scheduled to depart. Turns out my connection was delayed a half hour due to a radio issue so I got to the gate and the flight had even started boarding yet so everything turned out alright in the end.