You see why it's so naive and dangerous to use one translation to formulate doctrine? Or why it's dangerous to avoid determining word usage; Firstly, even if we go with the KJV, the term "might" (or even "may") is archaic [Old English] for have the ability. In fact, this is the very first definition in my M-W dictionary. But you're using the term in the sense of the third definition which is used to indicate possibility or probability .
Secondly, the Gr. term "sozo" (Strong's 4982) means:
sozo
NT:4982 sozo (sode'-zo); from a primary sos (contraction for obsolete saoz, "safe"); to save, i.e. deliver or protect (literally or figuratively):
KJV - heal, preserve, save (self), do well, be (make) whole.
(New Exhaustive Strong's Numbers and Concordance with Expanded Greek-Hebrew Dictionary. Copyright © 1994, 2003)
Of course, some of the the more modern translations (Formal and Dynamic Equiv. alike!) render v.17 on the order of the NIV:
John 3:17
17 For God did not send his Son into the world to condemn the world, but to save the world through him.
NIV
The ASV renders the last phrase "should be saved".
The AMP renders this phrase "that the world might find salvation and be made safe and sound through Him.
The TLB renders the phrase "but to save it".
The NASB, renders this phrase "that the world should be saved".
The TEV renders this phrase "but to be its savior", etc., etc.
Moreover, your interpretation would also contradict numerous scriptures that teach that God and his Christ are ACTUALLY saviors -- not merely potential or possible saviors. There are no scriptures that teaches that God is only a possible or potential savior.
It also contradicts a large number of scriptures that teach the doctrine of omnipotence. This doctrine teaches that nothing is impossible with God, nothing is too hard for him -- that nothing and no one can frustrate his eternal decrees. And this teaching comports very well with the definition of the Gr. term above, as well as many renderings that teach that essentially teach that Christ came into the world to [actually] save it. Did not Jesus teach that all the Father gives to him WILL [indeed] come to him (Jn 6:37)!?
Finally, your interpretation contradicts the two centeral OT passages that reveal God's New Covenant promises (Jer 31 and Ezek 36). Those promies are unconditional and unilateral in nature! God declares in those promises exactly what he will do for his people -- not what he "might" (or perhaps) do as you erroneosly interpet this term.