I wouldn't even use it to begin; return flight from CWL to either Chicago or Minneapolis using KLM or one of their partners for about 1400 pounds in July then connect with a direct flight to Vegas using Frontier or Spirit for about 350.
If you're not bothered about layover times to save cash, try Cheapoair website, they'll be heard to beat.
Agree wholeheartedly about spending time in the National Parks mentioned by Gofer, absolutely memorable. But if it is July / August you're thinking of take the trouble to book motels on your route to save having to sleep in the car