I've owned a .243, and the best I could get with factory ammo was about 1" to 1 1/2" on a good day, but like others have said it begins to open up unless the barrel is completely cool, and this was a standard contour.
It was O.K. for what I wanted to use it for, but I own other Handi's that are consistently more accurate, even after firing several shots through a warm barrel.
Now that Tim mentioned it, I did notice that the grooves in the rifling were shallower and less defined, on my particular barrel anyway, than any of my other barrels I own.
I think if I had hand loaded for it, I could have done better but I didn't, so I traded it away to someone that did, and never looked back.