You can do the Grand Canyon in a day, but it would be a very long day. Its about a 5 hour drive to the South Rim, each way, so you are looking at 10 hours on the road before you even factor in whatever time you plan to actually spend at the canyon.
If you are planning to do this as a one day trip, there are also bus tours from Vegas that would eliminate your need to do all the driving yourself, however, I would think you would have a better time simply doing an overnight trip, staying either at the canyon itself, or in nearby Williams or Flagstaff.