call him a cry baby and laugh at him.
I mean, er...
you can't please everyone all the time. Was this die roll in the open? If players are going to demand that a roll be done in the open, and it doesn't come up in their favor, you have a real problem when the disfavorable result is death. There is no satisfactory resolution. If the player KNOWS you cheated, he feels a little icky knowing his character didn't really make it. If you stick to the result, he dies. What do you do? In my opinion, the more satisfying (or rather, less dissatisfying) answer is to hold to the result, esp if it's a new character. He doesn't miss out on too much if he has to reroll the char, and you don't break form by ruining the game.
However, if they were less demanding of behind the screen rolls, they wouldn't have had the problem in the first place,a nd they need to realize it (preferably in a non-confrontational approach).
If the die-roll was behind the screen, I'd have cheated and let him live. He already had a weakened constitution. However, the damage is done either way now, and I'd stick to my guns. Nothing sends a gaming group in a downward spiral than a GM who will change the game or house rules retroactively. Change 'em on the spot while making the resolution? That's fine, as long as the results of the rule haven't applied and you've moved on. But if you HAVE moved on it's better to be consistant, maybe changing the rules for the future (and explaining that you will and why), even if the ruling was ultimately unfair.