Um, that's a good question dig. I've heard that question before, but never from the angle that you present it. I cannot give any definitive answer, and I'm not sure I should even try, seeing that I may confuse the issue even more. But I will make an attempt, and this is more me just putting some thoughts down and seeing what comes of them.
Let's start with John 15:15 since that's the first portion that came to my mind: "No longer do I call you servants, for a servant does not know what his master is doing; but I have called you friends, for all things that I heard from My Father I have made known to you."
This seems to suggest that, since Jesus only knows what the Father gives Him to know, Jesus is not omniscient and therefore not God. However, let's try to stay away from pulling one verse and forming a doctrine around it. Let's instead view everything within the context of the entire Bible and let other portions build and/or balance the idea that is presented in any specific portion (a very healthy and systematic way to understand the Bible).
Chalam has already given Philippians 2:5-11 so I won't quote all of it again. (Philippians is my favorite book btw; chapter 3 verses 12-16 is imperative to keep in mind as we seek to know God, for it keeps us grounded. If Paul didn't think he had reached a 'pinnacle' of knowing God, then why should we?) However look at verse 7. Quoting from the NASB, held by many Bible-wise people to be the most literal word-for-word translation yet, we get "...but emptied Himself, taking the form of a bond-servant, and being made in the likeness of men..." This portion in Philippians is the strongest evidence for the manifestation of God in the flesh, and one that I, as of yet, have yet to hear refuted. So what is meant by "emptied Himself"? First off, there must be something there to be emptied of. Secondly, it was only once He had emptied himself that He was able to come in the likeness of men. So by emptying Himself of His "godness" as it were, would not knowledge be a part of what was emptied? I can't say with certainty, but it does make sense. So being emptied of His omniscience, He was dependent on the Father (shown through His many prayers; which also gives us the example to follow) to reveal what was necessary for us to know; the knowledge of the "last day" not being a part of what we needed to know.
Not sure if that helps in any way or just muddies things more. If it's the latter, then I apologize; if the former, then thank God.
ps. The first five chapters of Hebrews present an excellent in-depth look at the person of Christ and the reason for the need of God to come in the form of man (Heb. 4:15 is awesome on this point!).
