Personally, I've never been caught. If I were, I'd just explain that I didn't mean any harm and just needed a place to sleep, and that I can leave immediately. In the US, unless there's a 'no trespassing' sign up, they have to tell you to leave and you have to decline before they can start shooting. They might call the cops and have them tell you to leave, but I don't believe most people would press charges over someone sleeping, unless of course it were marked or fenced property.
I try to stay on government property when ever possible, 10"-15" off the road, stick to an OG green bedroll, no fires, and not roll it out until after dark. Before dark, I might clear a space, cook a meal (alcohol stove) or heat some tea while I wait. Depending on where you're at, that's usually completely legal (until you go to sleep).