James 1:13, "Let no one say when he is tempted, "I am being tempted by God"; for God cannot be tempted by evil, and He Himself does not tempt anyone." It also says in Heb. 4:15, "For we do not have a high priest who cannot sympathize with our weaknesses, but One who has been tempted in all things as we are, yet without sin."
Answering this objection is a bit more difficult than answering the other objections to Christ's deity because it deals with an area of scripture that is not explicitly clear: the relation between the divine and human natures of Jesus. We see that Jesus has two natures as is taught in the chart below, but how they relate is not clarified in scripture.
Jesus as one person with two natures
He is worshiped (Matt. 2:2, 11; 14:33; 28:9)
He worshiped the Father (John 17)
We see from scripture that Jesus' human nature never existed apart from the union of His divine nature. We also see in scripture that God cannot sin, and that in Christ dwelt the fullness of the Godhead in bodily form (John 1:1, 14; Col. 2:9). Therefore, since we acknowledge that Jesus was divine, we could easily conclude that it was not possible for Jesus to have sinned. On the other hand, Jesus was truly man. Therefore, it is fair to say that Jesus could have been truly tempted. But, the question persists: if it was not possible for Jesus to have sinned, then how could He be truly tempted? I do not know if I have a sufficient answer to this, but I will offer one anyway.
First of all, is it possible for God to be tempted? Yes it is. Psalm 106:13-15 says, "They quickly forgot His works; They did not wait for His counsel, 14But craved intensely in the wilderness, and tempted God in the desert. 15So He gave them their request, but sent a wasting disease among them." (NASB). The Hebrew word for "tempt" here is nasaw. According to the Enhanced Strong’s Lexicon, it means to "to test, try, prove, tempt, assay, put to the proof or test." The NIV says, "they put God to the test." The KJV says, "and tempted God in the desert." The NKJV says, "and tested God in the desert." The 1901 ASV says, "and tempted God in the desert." Therefore, we can see that God was "tempted in the desert." Yet, this temptation in no way negates the divinity of God Himself.
In the New Testament, when Jesus is tempted in Matt. 4, the word for tempt is peirazo. Again, according to the Enhanced Strong's Lexicon, it means "to try whether a thing can be done, 2) to try, make trial of, test: for the purpose of ascertaining his quantity or what he thinks or how he will behave himself; 2c) to try or test one’s faith, virtue, character, by enticement to sin."
We can see in both cases that it was God who was tested. In the Old Testament, God was being tempted, that is, being put the test in the wilderness even as Jesus was being tempted (put the test) in the wilderness in the New Testament. This temptation can occur without God sinning. Furthermore, this temptation or testing is not a challenge to the deity of Christ any more than it was a challenge the the divinity of God in the Old Testament.
In addition, all that Jesus did, He did by looking to the Father. Jesus said, "Truly, truly, I say to you, the Son can do nothing of Himself, unless it is something He sees the Father doing; for whatever the Father does, these things the Son also does in like manner." (John 5:19). Also, Jesus said, "I can do nothing on My own initiative. As I hear, I judge; and My judgment is just, because I do not seek My own will, but the will of Him who sent Me." (John 5:30).
In Matt. 12:22-32 Jesus was casting out demons. The Pharisees accused Jesus of doing this by the power of the devil. Jesus replied to them that blasphemy against the Holy Spirit would not be forgiven. Why did he say this? I believe that it is because Jesus did none of his miracles out of his own divine nature but did them as a man working through and by the Holy Spirit who indwelt Him. Therefore, Jesus was casting out demons by the power of the Holy Spirit. We see that Jesus' miracles began after his baptism, and that is when the Holy Spirit descended upon him.
Jesus came as a man in order to fulfill the law of God and to be the sacrifice for sin. He did this as a man. When He resisted the temptations of the devil, He quoted scripture--as a man. He did not at that time rely on His divine nature when going about His earthly ministry in Israel. As a man, He was tempted; and as a man, He resisted temptation by relying on God's word. He cast out demons by the Holy Spirit and not by His own divine nature. Therefore, Jesus was tempted in His human nature--not in His divine. He did not rely on His divine "side" to help Him out. Instead, He completely relied on the Father, the Holy Spirit, and God's word to successfully resist the temptations that came to Him.
Therefore, I conclude that Jesus could not have sinned, but that He could be tempted; that is, He could have a sinful option presented to Him--as was presented to God in the wilderness--yet Jesus would not have sinned.