The verse begins, “No man…” (Gk. οὐδείς). This is what is called a universal negative, which means that every member of the class is excluded. What, then, is negated with reference to all humanity? Well, it is “can” (δύναμαι). This term denotes ability. Consider the BDAG definition, the standard of Greek lexicons: “to possess the capability (whether because of personal or external factors) for experiencing or doing something.” So, what do we have thus far? You could say it many ways. But simply put it means that no person has the ability or capability to experience or do something, namely what follows in the verse—“come.”
Therefore, as it is, John 6:44—so far—means that no person (universally) has the capability to come to Jesus. This seems to lead to a dire circumstance. Thankfully, there is an exception.
That exception is “except” or “unless” (ἐὰν μή). This conjunctive particle prepares the way for a condition. Hence, no person has the capability of coming to Christ, unless...something. That something is, if and only if the “Father who sent me draws him.” So, the Father’s drawing is the only condition that excepts humanity’s universal inability to come to Christ.
The term “draw” (ἕλκω) cannot be reduced, as is often done by Arminians, to mean “woo” or charm or some such thing. It connotes an external force of power with the passivity of the object. For example, “Simon Peter went up, and drew (ἕλκω) the net to land full of great fishes” (Jn. 21:11). “Do not rich men oppress you, and draw (ἕλκω) you before the judgment seats?” (Jas. 2:6). “They caught Paul and Silas, and drew (ἕλκω) them into the marketplace unto the rulers” (Acts 16:19). “And all the city was moved…and they took Paul, and drew (ἕλκω) him out of the temple” (21:30). You see, then, it is not by the power of the object of ἕλκω that is intended but its subject, according to biblical usage.
Therefore, John 6:44 means that no person has the capability of coming to Christ, except or unless the condition of the Father’s drawing occurs. Who, though, does the Father draw? According to Jesus in John 6:37, “All that the Father giveth me shall come to me; and him that cometh to me I will in no wise cast out.” “All” indicates another universal. In this case, it is a universal affirmative rather than negative, as in v. 44. All of those given by the Father to the Son will come. Therefore, to state it negatively, none of those who do not come were given of or drawn by the Father to the Son. Therefore, all and only those given to the Son by the Father (i.e., the elect) will come to Christ, which God makes possible by doing that which is humanly impossible, giving them the ability to come, thus drawing them. That is what John 6:44 means, which is exactly what many claim, “No, it does not.”
Some respond by invoking John 6:45, “It is written in the prophets, 'And they shall be all taught of God.' Every man therefore that hath heard, and hath learned of the Father, cometh unto me.” In so doing, they want the word “all” to ring in the ear. This is a citation of Isaiah 53:14, however, which was originally and exclusively spoken to Israel, the elect, which confounds their case. Moreover, it is begging the question. What is the antecedent for “they” in v. 45? It is the “given” ones of v. 37, the “drawn” ones of v. 44. Therefore, it is fallacious in the highest degree to appeal to v. 45 to tell us who those are in v. 44, since v. 44, according to the most basic principles of grammar and hermeneutics, tells us who those in v. 45 are—the elect.