staving off defeat

What do you mean incorrect insufficient material?

You moved last, so your opponent must have run out of time.

Normally you win when your opponent runs out of time. But you had insufficient material to checkmate your opponent.

Therefore, the game is drawn by insufficient material.

Ivandh must be right. It was Black who had insufficient mating material when White ran out of time. Thanks for clearing that up; it was a real mystery

As to the game itself, I think your troubles actually started with 3...e6. Not because this is a terrible move, or because White now has a big advantage, but because you are starting down the wrong path. Wouldn't White love to have two pawns abreast on d4 and e4? Of course he would! This gives him the kind of big center you don't get in a mainline Sicilian. And doesn't White's pawn on c3 prevent his normal Nc3 move? Sure it does. So don't play this like a routine Sicilian; there are significant differences. The first move that comes to mind for you is 3...Nf6, taking advantage of the fact that he can't protect his e-pawn with the normal Nc3. After 4.e5 Nd5 5.cxd3 c3, White's dream of a beautiful pawn center is but a memory and you are getting close to equality. Your work isn't done--there's still a tough struggle ahead--but you're fighting. 

4...d6 isn't a bad move, but once again, you're not exactly challenging White's buildup, are you? And why fear e5 from White? He gives up his ideal pawn center, and you can start undermining his e5 pawn with d6. Every pawn advance isn't a threat!

I've wasted quite a bit  of space on the the first few moves of this game because I want to emphasize that the game starts on move one! You can't just "develop" your pieces and then look around for a plan.