the mass of an object, and all objects produce a field of gravity. that is besides the point.
what jebus was pondering was what would happen to a person at the very center of the earths gravity and there was a hollow airspace at the center to make this possible.
now all the earth's gravity is 'pulling' towards the center as you correctly state. this is what anyone can learn from a science book. now try and take a step off some author's shoulders and think for yourself with a little imagination for a change.
'Pulling' denotes that you have seperation between yourself and an object. if you have a ball on a string 10ft away you can pull it right on to you. when the ball gets to your fingers you cannot 'pull' the ball any further unless you move your hand seperately from the ball, or the other way around....or both at the same time. i dont think the earth will be planning any vastly new orbits for the remainder of the suns life.
so when you are 'pulled' to the very center of gravity and gravity is acting all around you from every direction it simply cannot be 'pulling' you any further without moving the whole earth or you seperately.
so we can only assume that gravity when completely surrounding you from all directions to remain static could be considered the only possible 360 degree 'push' gravity can produce. just call it negtive scale zero gravity and i think that yes you would just float there, like jebus first said. in space you float because surrounding gravity fields are so weak, inside the center of a huge gravity field you float from 100% concentration of the gravity's source.
but hey, i have only given the topic a half hour of thought. i could always be wrong although hell, it looks good from where i wrote it.