As God, yes, but not as man, thus therein lies the possibility.
Luk_1:37 For with God nothing shall be impossible.
Mar_14:36 And he said, Abba, Father, all things are possible unto thee; take away this cup from me: nevertheless not what I will, but what thou wilt.
Then are the verses (Hebrews 6:18; Mark 14:36; Luke 1:37, see also Matthew 19:26; Mark 10:27; Luke 18:27, etc) in contradiction? No. They are in harmony. Notice, the statements, carefully:
Heb 2:9 But we see Jesus, who was made a little lower than the angels for the suffering of death, crowned with glory and honour; that he by the grace of God should taste death for every man.
Heb 2:10 For it became him, for whom are all things, and by whom are all things, in bringing many sons unto glory, to make the captain of their salvation perfect through sufferings.
Heb 2:11 For both he that sanctifieth and they who are sanctified are all of one: for which cause he is not ashamed to call them brethren,
Heb 2:12 Saying, I will declare thy name unto my brethren, in the midst of the church will I sing praise unto thee.
Heb 2:13 And again, I will put my trust in him. And again, Behold I and the children which God hath given me.
Heb 2:14 Forasmuch then as the children are partakers of flesh and blood, he also himself likewise took part of the same; that through death he might destroy him that had the power of death, that is, the devil;
Heb 2:15 And deliver them who through fear of death were all their lifetime subject to bondage.
Heb 2:16 For verily he took not on him the nature of angels; but he took on him the seed of Abraham.
Heb 2:17 Wherefore in all things it behoved him to be made like unto his brethren, that he might be a merciful and faithful high priest in things pertaining to God, to make reconciliation for the sins of the people.
Heb 2:18 For in that he himself hath suffered being tempted, he is able to succour them that are tempted.
Yes, Christ Jesus took upon Himself the likeness of sinful (fallen) flesh (Romans 8:3, etc). Yes, Christ Jesus, as a man, could be tired (Mark 4:38), be hungry (Luke 4:2), be sorrowful (John 11:35), be thirsty (John 19:28), be angry (Mark 3:5), be in pain (John 11:33), and so many other things which pertain to the nature of sinful (fallen) flesh, as Hebrews 2:10,16,17 reveals.
Yet, none of that is being "tempted". Temptation (testing or tried) is not being led to be "tired", "hungry", "sorrowful", "thirsty", angry", in "pain", and so many other things of the experience of the likeness of sinful (fallen) flesh.
Heb_4:15 For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin.
The devil's temptations to Christ Jesus, was not to be hungry, etc. Jesus was already hungry, being led of the Holy Ghost into the wilderness. The Temptation that came from Satan to Jesus ,was that Jesus might violate God's Character, Law, Kingdom in the slightest way and so sin.
The very words "being tempted" (being His; vs 18), in connection with those "that are tempted" (us), is found in the previous verse, verse 17, dealing with temptation to "sins". It is the same in Hebrews 4:15.
We are not tempted to be tired. The Bible says that the spirit is willing but the "flesh is weak" (Matthew 26:41). Tiredness, Hunger, Thirst, etc are merely result of existing in the likeness of sinful (fallen) flesh, and in this fallen world. The real and actual temptation, is to violate God's Character, Law and Kingdom - thus sin.
1Co 10:12 Wherefore let him that thinketh he standeth take heed lest he fall.
1Co_10:13 There hath no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that ye are able; but will with the temptation also make a way to escape, that ye may be able to bear it.
1Co 10:14 Wherefore, my dearly beloved, flee from idolatry.
It is
no temptation to be hungry, tired, sorrowful, angry, etc. It is temptation to violate a command of God (such idolatry), and so sin against God. Eve was tempted, sinned and fell, by idolatry. Notice, it is
"common to man" (ie the nature of mankind), and Jesus was found in the fashion as a
"man" (Philippians 2;8).
It is true, that in Christ Jesus (the last Adam) was no propensity to sin (even a the first man Adam had none), as we now have (since we have already sinned; Romans 3:23). But that is not to say that Christ Jesus was not made fully in the likeness of sinful (fallen) flesh and tempted to be as us, a sinner (for that which is flesh is flesh and that which is spirit is spirit, as per John 3, etc; for Jesus was born of Mary (flesh, ancestry of fallen seed/flesh of David) of the Holy Ghost (Spirit)). He was made to be sin for us, not made a sinner. Sin is a choice of the will to do or not do as God commands (1 John 3:4), not a state of being.
When the devil tempted Jesus in the wilderness, what was the devil tempting Jesus to do? Notice, not 'to be', but 'to do'. It is not temptation to be "hungered", or "thirsty", etc.
Mat_4:1 Then was Jesus led up of the Spirit into the wilderness to be tempted of the devil.
Luk_4:2 Being forty days tempted of the devil. And in those days he did eat nothing: and when they were ended, he afterward hungered.
If we say that the devil was tempting Jesus to be hungry, then it implicates God, for it was the Holy Ghost that led Jesus into the wilderness and to be hungry. So, while it is true that "God" cannot be tempted, "man:" can be, even as James states clearly (James 1:13-14). Jesus was "tempted" not as "God", but as "man". This was the trial.
