My very first experience of giving head was just such an occasion... I was not long past the age of consent in the UK (younger than the US I believe)... I had a steady boyfriend but i'd saved myself until 'of age'. We were in my parents small closed porch and I obliged him with a rather naive and 'toothy' BJ.... he seemed huge at the time but later partners proved he was probably actually about average. Anyway, i'd never even seen a guy cum, let alone experience it myself, so I rather stupidly agreed to let him go off in my mouth, for the sake of cleanliness. I eventually felt what I now know to be the tell tale signs of tensing, twitching of balls and cock as he reached climax, but was completely and utterly unprepared for the sheer volume of cum and the force with which it exploded down the back of my throat, he then kept cumming and cumming, spurt after spurt, as it filled my mouth and overflowed down my chin and blouse.. still in shock I managed to swallow as much as I could but there was a significant amount down me... and I still had to run the gauntlet of getting past my parents to my room without them noticing... lol. I remember being very angry with him because he must have known how much he was going to produce and didn't warn me, but all he did was grin back at me with a really smug self-satisfied look on his face... arsehole...;-). We didn't stay together very long after that.
On reflection it may not have been the sheer volume of cum that caused the inability to swallow it all and resultant spillage, more likely my naivety and unpreparedness... I've never had the same problem again. ;-)