Welcome along srt8!
As frankvb says, if you are travelling on one booking reference then you really should have little or nothing to worry about. You also have the possibility that your 279 will be early and the almost certainty that your UA connection to LAS will be late!
As he also says, US carriers are often quite flexible about just moving you across to the next available service and, within the last 8 months, I've had US agents issue a boarding card for a flight to DFW and then onward to PHX that I personally/physically could make, but that they knew the bags wouldn't.
The bags followed on a different route and rocked up in PHX 35 minutes after I did. It would never happen here, but all sorts of crazy things still do there.
Worry not a lot.