Depending on the state, the rules regarding sleeping in rest areas vary greatly. I seem to recall that Utah and Nevada had a 24-hour limit. Others are shorter, but all of them are intended for those who need to sleep before driving further. If you're not safe to drive because you're too tired, they're not going to make you move. I've never been disturbed even when I parked in a short-term space all night.

However, due to the extreme transience of the traffic through a place like that, it isn't the safest place to choose to sleep. Take a hint from a seasoned traveler: If I have to stop at a rest area I park right smack in the middle, up front, right UNDER a streetlight. What you realize pretty quickly is that if you're off at the edge, the streelights are going to shine sideways in the windows and be bright in your eyes. If the light is directly overhead, everyone outside can see your vehicle easily (disuading robbery) but it keeps the light out of your eyes.

SRS