I agree with the above, and have seen it happen a few times.
Another problem that generally arises in 1 player running multiple characters (and one that comes up more often in my experience) is that the player might end up only roleplaying one of the characters (speaking through this one character, having a fully developed personality and background for him, and interacting with the group only with him), while the other character just becomes a list of extra stats and powers that the group can pull out whenever they need them.
Its best if the players each make up one fully developed and thought out character, and worry about playing him/her well. Its really hard to run 2 completely different characters at the same time, without falling into the "Main Character"/"Backup Character" problem.
I'd say, unless you think your players are capable of portraying 2 separate human beings believably, at the same time, don't let them play multiple PC's.
If the PC group ends up not having certain skills/powers that might be useful in the story, thats a perfectly good opportunity to force them to jump through hoops to convince an NPC that has those gifts to help them.