No! Gods sovereign will is...we don't have a choice, No where in scripture does it teach Gods will is that you have to make a choice!
If you have the choice to accept or reject it, then it is not a gift, but an offer, only good upon your accepting, and of course you can reject an offer.
Can you unchoose Christ's death and resurection?
If I were a multi millionaire and came to your birthday party and the gift I gave you was a million dollars in cash...
...You don't have a choice to accept it or reject it.
It's Yours! It's a gift! Not an offer!
Who in their right mind would reject a million dollars?
Besides the Jews?

and unbelievers!
As I have stated before, you have got to get away from this offer /choice understanding of salvation...it is a declaration of salvation. A declaration of something is not up for grabs, take it or leave it choices...like taxes...it has been declared you will pay taxes.
Although I do like the offer/choice option of paying taxes.

But I have no choice.
God does not give a gift and then says, but its conditional upon you. Yet it is conditional upon Him giving it, but unconditional to those whom he gives it too, and He gives it to whom He wills.
Unless your will trumps Gods? I Don't think so!
If you have been given the free gift of salvation, why in the world would you want the choice to give it back? Pretty silly, Eh! OK so you want the choice, so what are you going to do...choose to go to hell?
That should cause your heart much rejoicing...you can't give it back!

(unless it was never given to you in the first place)
Who wants a God that would give us a choice to say ...NO, don't save me unless I give you my permission?
When your children were born, aren't you glad you didn't have to make the choice to keep them or give them up for adoption? Don't dare you say...but I did have a choice...tell your wife that and see what happens! I'm sure she has a favorite name for you.
Now go and tell every one how this multi-millionaire gave you a million dollars in cash, Give it away one thousand dollars at a time if you like. And whoever says, Ooohhh, let me decide if I can accept it, just move on and give it to someone else and let the dead bury the dead.
And this is why we evangelize, we don't know whom knows a free gift when they are given it and those whom have to make a choice to receive it. We just know that all whom God has appointed to eternal life will rejoice in it when they have it and it's not up to us to make sure the anyone gets it. Yet all of it is the Spirits work. With out the Spirit, there would be no Preaching, Evagelizing, Receiving or Rejecting, and there is no chioce upon whom, when or where the Spirit works.