The word draw us as stated in John 6:44 No man can come to me, except the Father which hath sent me draw (Gk(drag) him: and I will raise him up at the last day.
The words translated "draw" and "drew" in the Greek New Testament are HELKUO and HELKO. Each of these words has the basic meaning of "compel ... .. draw," "pull," and "tug." In most instances the force which does the drawing or compelling is sufficient to cause the object of the drawing to respond fully.
Notice the context of the folowing verses.
Eph 2: 1(1) And you hathhe quickened, (2) who were dead in trespasses and sins;
QUICK ."Quick means living and active — LIFE-GIVING! "For the word of God that speaks is alive and full of power — making it active, operative, energizing and effective; it is sharper than any two-edged sword" (Heb. 4:12, Amplified).
2Wherein in time past ye walked according to the course of this world, according to the prince of the power of the air, the spirit that now worketh in the children of disobedience:
3Among whom also we all had our conversation in times past in the lusts of our flesh, fulfilling the desires of the flesh and of the mind; and were by nature the children of wrath, even as others.
4But God, who is rich in mercy, for his great love wherewith he loved us,
5Even when we were dead in sins, hath quickened us together with Christ, (3) (by grace ye are saved
6And hath raised us up together, and made us sit together in heavenly places in Christ Jesus:
7That in the ages to come he might shew the exceeding riches of his grace in his kindness toward us through Christ Jesus.
Finally man is in the picture.
8For by grace are ye (4) saved through faith; (5) and that not of yourselves: it is the gift of God:
9Not of works, lest any man should boast
I will add once this has happen we had no choice or freewill.