Maybe I am wrong, but I always assumed that this quote refered to Dalinar. He promises to Kaladin that everything is going to be allright, that he will take care of Kaladin and his men. And then, Sadeas refuses to sell them. Dalinar has told Adolin that this should not end in a bloodbath, and that protects Sadeas (He will have no chance against two shardblades if they (Dalinar, Adonlin...) were determined to kill him, even being in so bad shape (At least that is what I think).
So,
"All is withdrawn for me. I stand against the one who saved my life. I protect the one who killed my promises. I raise my hand. The storm responds."
I stand against the one who saved my life (Kaladin, who has returned because of the promises made by Dalinar)
I protect the one who killed my promises (Sadeas, who refuses to sell bridgemen)
I raise my hand. The storm responds. (Dalinar summons the Shardblade, which is a price Sadeas can't refuse).
The storm as similar thing to the mists in mistborn has been discussed, thus my thoughts of "The storm responds" being the summoning of the blade.
Ok, now, two things
1.- Forgive any mistakes in my english, as usual
2.- Sorry about the interruption, but as I said, I always had believed that this quote refered to Dalinar, but seems that I am alone...