I have played this line as black once some years ago against an opponent who is now an international master and his opinion and mine after the game was drawn (I was rated 500 point below him) is that is absolutely nothing like a winning attempt for white.

For one pawn, black as the bishop pair, a better development and a very easy game.
White, on the other hand, has a pawn, difficulties to develop in an acceptable way and the obligation to parry the uncoming threats that black will be able to generate.

It's not so much a question of beating off black's attack than trying to play a coherent game for white.
Black is not on a ruch to attack, he has more than enough compensations and they won't go away.

You should look at some games with this line, in particular Karpov-Larsen who will show how even Karpov can lose without black having to find anything extraordinary.

How does white best beat back black's attack after
1.e4 e5 2.Nf3 Nf6 3.d4 Nxe4 4.Bd3 d5 5.Nxe5 Nd7 6.Qe2 Nxe5 7.Bxe4 xe4 8.Qxe4 ?

I know this line is supposed to be fine for black but given the imbalance it seems to be a good place to fight for a win as white. 

Also, if your a pawn up and not currently in checkmate you must be better.