Wrestling With the Watch Tower: Jesus, the Firstborn of All Creation

The Jehovah's Witness at the Christian's door, if pressed to defend the position that Jesus is not God but is instead His first creation, might start with Colossians 1:15 which reads, "[Jesus] is...the firstborn of all creation" (in certain translations including the NASB and Watch Tower-approved NWT). The argument is presented in the Watch Tower publication, "What Does the Bible Really Teach?" in the chapter, "Who is Jesus Christ?" in the section, "Where Did Jesus Come From?" (http://www.watchtower.org/e/bh/article_04.htm):

Jesus is Jehovah’s most precious Son—and for good reason. He is called “the firstborn of all creation,” for he was God’s first creation. (Colossians 1:15)

The dictionary defines "firstborn" as, "first in the order of birth; eldest" or "a first result or product." The Watch Tower's argument, then, is that in saying that Jesus is "the firstborn of all creation" Paul is asserting that of everything God created, Jesus was the first. Obviously, if Jesus was created by God, He is not God Himself, and does not have an eternal nature but instead came into existence when the Father created him.

But is this in fact what this passage in Colossians teaches?