Rarely--but a food item that is too big for the snake would be much larger than the snake is around at its thickest point. We use that as a standard measurement because it's a size that is actually easy for the snake to handle and digest--they can eat something much larger than that.

This snake ate a huge meal successfully: http://img.thesun.co.uk/multimedia/a...82_443404a.jpg

So did this one: http://www.cairns.com.au/images/uplo...6/snake320.jpg

And this one--a skinny rat snake swallowing a huge rabbit: http://www.tanwater.com/wildlife/flo...0snake_105.jpg

None of them had problems with these meals--snakes are well designed to eat big prey items. It is more difficult for them to digest a really big meal, and it takes them longer.

This python DID swallow more than he could handle:
http://www.cryptozoology.com/forum/i..._copy_4573.jpg
Considering how sturdy alligators are, perhaps the alligator wasn't entirely dead when it was swallowed, which might have contributed to this result. If it started moving after it was swallowed, it might have caused internal trauma, and led to this.

Notice that the snake swallowed the entire alligator, down into its stomach, before it had a problem--the skin of their neck and esophagus is enormously elastic. So don't worry about that--no prey item only as big around as your snake is ever going to cause an issue passing through their throat.

Most snakes will not eat something they judge to be too big--it's extraordinarily rare for their judgement to be so bad that they eat something that bursts their stomach. It's more common for a snake that has eaten something too large to regurgitate it without suffering harm.
But in most cases they won't eat anything they can't handle in the first place.