So human analogy time:
You are poor, starving and do not have shelter. You inheritted a million dollars. It is in your bank to spend, no catches, you even have a debit card so you can take it out. You are so used to being poor, starving and not having shelter, that you have a choice when I tell you the good news, you have a million dollars!
If you believe me, you use the million dollars, you won't be poor, starving and homeless. If you don't believe me, you are still starving and homeless, even though you are not poor anymore.
So he who believes is saved, he who doesn't believe is...what?
The problem doesn't come in the words, it comes in how you percieve the words. If you think it was an ultimatum, then you have read it wrong. Whether you believe or not, does not nullify the good news. Whether you accept it and apply it in your life, is what Jesus was talking about.
1 Corinthians 3:10-15
By the grace God has given me, I laid a foundation as an expert builder, and someone else is building on it. But each one should be careful how he builds. For no one can lay any foundation other than the one already laid, which is Jesus Christ (THE GOOD NEWS!). If any man builds on this foundation using gold, silver, costly stones, wood, hay or straw, his work will be shown for what it is, because the Day will bring it to light. It will be revealed with fire, and the fire will test the quality of each man's work. If what he has built survives, he will receive his reward. If it is burned up, he will suffer loss; he himself will be saved, but only as one escaping through the flames.
The problem now comes in, if you don't believe in free-will, there is no need for a great commission. If you don't believe in a free-will, then you don't have to worry about being careful in what you build. Does that nullify that in the end all mankind is saved? No. It means that everyone who is pre-destined from the beginning to the end, but the journey is where we build and store either treasures on earth, or treasures in heaven.