I wouldn't, it'll probably fall off the jack. If I tried it, I have all 4 tires on it just in case...

 

if its a good floor jack, not one of those little skinny cheap ones, absolutely. ive moved and seen cars moved this way many times, its not going anywhere, unless you have lots (i mean lots!) of free movement in the front springs.
just pick it up just high enough to keep it off the ground, point the jack the way you want to go, and move it. it really helps to have an assistant pushing as well as you pulling. we used to move cars around like this at the shop i worked at and the body shop we painted my first camaro at, works like a charm for moving cars stacked two/three deep sideways, so you dont have to move every car outside to reposition.
oh yeah, "meatball" huh? never heard that before, must be an eastcoast thing, on this side we usually refer to them as a pumpkin.

 

I do it all the time. It works best by pulling on the jack, not pushing, and have a helper push the body of the car.

Edit: I just saw 68rs406's reply, sorry for the duplicate post..

 

Done it many times and I've always found it easier to pull the jack also. Make sure you're using a good floor jack just like 68rs406 said, one of those cheap skinny ones is asking for trouble.

Stephen

 

East coaster here and I always heard it called a pumpkin or jackpot.

Anyway, be sure your floor is swept clean and watch foe cracks too. I always pulled the jack too.