I understand that the argument for an Aramaic original for Matthew comes from a fragmentary reference by Papias. He says that Matthew wrote a gospel in Aramaic and that Papias and the other Greek-speakers do their best to struggle through it.
However, the text we have as the Gospel of Matthew does have some features inconsistent with an Aramaic original. One, it is Synoptic, and since Q has never bothered to demonstrate its existence in the manuscript evidence, the best hypothesis we have to go on now is Markan priority. Two, the text includes a stylistic feature on a couple of instances whereby it transliterates a word or phrase directly from Aramaic, and then explains the meaning to the Greek reader. Based upon these, I find it unlikely that the Gospel of Matthew we have is the one Papias was writing about.
Naturally, the actual sayings came out of Jesus' mouth in Aramaic. I remember reading a debate between Ben Witherington and some Reformed guy about the proper way to render the Aramaic behind the Greek in Jesus' words. BW3, who usually is unassailable in his reasoning, here tried to argue that we should assume the Gospel writers used a formal-equivalence translation of Jesus' literal words into Greek, and therefore we should reconstruct Aramaic verb forms within that paradigm (this was specifically applied to Jesus' discourse to Peter about binding and loosing things in earth and in heaven). The Reformed guy rightly pointed out that doing exegesis based upon such a speculative assumption as Mark's translation philosophy is utterly spurious.
But this does bring up a question in my mind regarding verbal plenary inspiration. Which is moreso the inspired inerrant Word of God, the verbal Aramaic words coming off the lips of the Son of God, the Word made flesh, or their translation, literal, dynamic, or whatever else, into Greek in the original autographs of the New Testament?