Two thoughts:

1) If the first flight is delayed such that you miss your connection, Delta will automatically rebook you. Of course, you might not like your new route, seats, etc, but they'll get you to your final destination. And depending on how serious a delay it is, you might be eligible for food vouchers etc. But, a good first step would be to know what your preferred rerouting would be, and have that info when you call them (should your flight be delayed). And, yes, in general, the sooner you call once you know there's going to be trouble, the better. Or go to the airport even since the gate agents are likely to be able to help whereas someone on the phone might not.

2) If you ask to get on another flight, they'll charge you $150 for the change fee plus the difference in cost of the ticket. Simply not worth it, I think, but that might depend on how vital it is that you get to LAS on time.

Also, it's not totally clear from your e-mail but it sounds like you might be on an award ticket (i.e., you used miles to get the ticket rather than paying cash), in which case your rebooking options are even fewer within a 72-hour window due to recent DL policy changes (you can read a lot about those changes elsewhere on FT).