The Christian argument here is that the verse speaks of someone who has been pierced, and Jesus was pierced so the verse must refer to Him. Critics claim this doesn't fit the context and that the piercing must take place after the events described in verses 1-9.

Let's take a look at verse 10 once more:
> "And I will pour upon the house of David, and upon the inhabitants of Jerusalem, the spirit of grace and supplications: and they shall look upon me whom they have pierced, and they shall mourn for him, as one mourneth for his only son, and shall be in bitterness for him, as one that is in bitterness for his firstborn."

The context actually indicates that the MOURNING over the one that they pierced will take place after this event. This is understood in many circles to refer to the heralding of Christ's 2nd coming at the end of the world. The Jews (or many at least) will mourn for the one that they pierced (Jesus) and will be cleansed of their sins for accepting the Messiah. The context of this verse indicates that the Jews will be looking back on a past event, and this need not be immediately after the piercing takes place.

There is also an objection regarding translation. The Hebrew word rendered as "pierced" is dakar, which usually has the implication of stab or run through with a sword. We see no reason here that dakar cannot mean "the stabbing" or "to run through" flesh with a spear or nails as occurs in crucifixions.