Calvinists often use John 6 as a proof text to support their premise, but doesn't it help to understand WHO Christ may be referring to when he speaks of those who have been given to him?
Let's read later in the name gospel (chapter 17) where Jesus clearly shows us what he is speaking about when He speaks of 'those thou hast given..."
6 I have manifested thy name unto the men which thou gavest me out of the world: thine they were, and thou gavest them me; and they have kept thy word.
7 Now they have known that all things whatsoever thou hast given me are of thee.
8 For I have given unto them the words which thou gavest me; and they have received them, and have known surely that I came out from thee, and they have believed that thou didst send me.
9 I pray for them: I pray not for the world, but for them which thou hast given me; for they are thine.
10 And all mine are thine, and thine are mine; and I am glorified in them.
11 And now I am no more in the world, but these are in the world, and I come to thee. Holy Father, keep through thine own name those whom thou hast given me, that they may be one, as we are.
12 While I was with them in the world, I kept them in thy name: those that thou gavest me I have kept, and none of them is lost, but the son of perdition; that the scripture might be fulfilled.
13 And now come I to thee; and these things I speak in the world, that they might have my joy fulfilled in themselves.
14 I have given them thy word; and the world hath hated them, because they are not of the world, even as I am not of the world.
15 I pray not that thou shouldest take them out of the world, but that thou shouldest keep them from the evil.
16 They are not of the world, even as I am not of the world.
17 Sanctify them through thy truth: thy word is truth.
18 As thou hast sent me into the world, even so have I also sent them into the world.
19 And for their sakes I sanctify myself, that they also might be sanctified through the truth. {sanctified...: or, truly sanctified}
20 Neither pray I for these alone, but for them also which shall believe on me through their word;
21 That they all may be one; as thou, Father, art in me, and I in thee, that they also may be one in us: that the world may believe that thou hast sent me.
22 And the glory which thou gavest me I have given them; that they may be one, even as we are one:
23 I in them, and thou in me, that they may be made perfect in one; and that the world may know that thou hast sent me, and hast loved them, as thou hast loved me.
24 Father, I will that they also, whom thou hast given me, be with me where I am; that they may behold my glory, which thou hast given me: for thou lovedst me before the foundation of the world.
25 O righteous Father, the world hath not known thee: but I have known thee, and these have known that thou hast sent me.
26 And I have declared unto them thy name, and will declare it: that the love wherewith thou hast loved me may be in them, and I in them. (Joh 17:6-26 KJV)
Clearly, those given to Christ while on earth were the appointed messengers of Israel who were to fulfill the purpose of Israel's election by taking the message of redemption to the world. The rest of Israel was being hardened (John 12:39) which is why they were unable to come to Christ. It was only after Christ was lifted up that he sent these appointed messengers (and the Spirit to indwell them) to proclaim the gospel, by which he would 'draw all men to himself.' (John 12:32)
This is the context in which we must understand John 6.