I made a 60 minute international to domestic connection at DFW. I arrived from into DFW from SCL at 6:40AM and made it to my 7:40AM flight to SJC with time to spare for a trip to the AC.
It definitely helps to be towards the front of the plane, regardless of cabin, and to be a quick walker. Customs was quick since I was at the front of the pack. You will have to go through security again like other posters have said. The recommendation to walk to the next security screening area if the first one is a zoo something to keep in mind.
I did not check bags so I had no experience whether checked luggage would make the transfer in those 60 minutes.