What do you mean by "same spot"? Relative to what? The sun? The galactic center?

I'm going to assume you mean the standard "what would happen if I hovered in a helicopter for hours, would I be somewhere else?"

No. You are moving right now. When a helicopter (or you) hovers, it is matching the rotational speed of the ground below it. Let's say what you mean is that you take off at sunrise and for 12 hours you want to keep the sun at the same visual spot on the horizon. You would no longer be hovering because you would have to counter your current speed, meaning you would have to race West at something like 1000 miles an hour. You have to counter the rotational speed of the earth at your latitude and I believe if you do this at sunrise, you don't have to add the Earth's speed around the sun, you just have to maintain your elevation because the earth is moving toward you as it sounds beneath you.