Well it sounds like you're looking for a reason to miss your flight. If it is delayed and you legitimately miss it, then you'll be taken care of. But if it arrives in plenty of time and other pax make it but you are the last one to arrive, then there could be an issue since it may seem obvious and not Delta's fault.
In a misconnect event, they will try to rebook/reroute you to get you home the same day. If there are no options left for that day, then it would be the next day.