If someone had the ability to jump up into the air and stay in that exact same spot, would the world pass under their feet in 24 hours?

My guess, yes.

I think the ability would have to include jumping forward at a great velocity to counteract the Earth's rotational velocity. For instance, if you jump straight up at the equator, you land at the same spot even though the Earth is rotating at 1,000 miles per hour there. So the feat of such a jumper, who must jump forward at 1,000 miles per hour and maintain speed for 24 hours, might not seem so amazing. Some people might mistake the jumper for a jet. :)

If you were able to stay in the exact same spot for 24 hours, not only would the world pass under your feet (unless you get hit by a building), the earth would move 2 and a half million kilometers (about 1.6 million miles) away from you as it goes around the sun.

The sun itself would move 19 million kilometers (about 12 million miles) away from your position as it turns around the center of the galaxy.

And that doesn't take in to account the continual expansion of the universe because of the big bang.