"Limited" is not the best way to describe Atonement, because both those who believe in elective salvation and those who believe in free-will, limit the Atonement in some way. Calvinists limit it by saying that Christ's death was only for the salvation of the elect. Arminians - and all of those who believe that we have free-will in the matter of salvation - limit the Atonement as well. How so? Sure, the Atonement is for all, you would say, but it doesn't save any single person. It is limited.

So the Calvinist limits it by making it refer to a few, but saving those thoroughly. And the Arminian (and all other free-will believers) limit it by not believing the Atonement can save anyone.

Arminians require that the believer reaches up to God with their faith in order to make the Atonement "work". In other words, their response, their faith, is the active ingredient that makes it all come together. This makes man, and not God, the deciding factor in his own salvation. Often in the tracts and literature of today you will find some plea to the unsaved that runs like this: "God has done His part. He sent His Son to die on the cross for you. Now you need to do your part and reach out in faith and accept the free offer of salvation."

By contrast, Calvinists do not believe that there is a "God's part" and a "man's part": Salvation is All of God. Even the faith to believe was a sovereignly-planned gift given only to the elect so they would believe savingly in the good news.

The Reformed (Biblical) position is that every person that Christ died for was/will be saved in the fullest sense of the word (see Romans 6:1- 7). The Atonement in Christ's death - as far as the elect are concerned - far from being limited, is powerful because of this fact. The imagined free-will Atonement is indeed limited as far as the elect are concerned, because something (our faith) must be added to it to make it reach us.  

Believers in Free-will recognize the incongruity of that teaching with election, but leave it as a mystery. There is indeed mystery in this subject (Romans 11:33), but it isn't ALL mystery. It is up to us discover where mystery ends and generic illogicality begins. If you believe in free-will - the kind that choose God in any way - it might be good to ask yourself what verse actually proves that.

There are many verses that show that God commands all to repent like Acts 17:30:

"In the past God overlooked such ignorance, but now he commands all people everywhere to repent."

But God saves only some. This is something that is clearly taught in Scripture. The root cause of God not saving all is not because they would not turn to God in repentance. The root cause is that they were not chosen in the first place. They cannot even hear what God is saying because they do not belong to God. This is shown by this passage (John 10:26 - 27):

"but you [referring to unpersuaded Jews] do not believe because you are not my sheep. My sheep listen to my voice; I know them, and they follow me."

If Arminianism (or any form of Free-willism) was true, Jesus would have reversed the order, saying,

"You are not my sheep because you do not believe". (Not in the Bible)

All they would have to do would be to believe and they would become His sheep. All they would have to do is believe and the effects of the Atonement would be theirs. This is Arminianism, though it is known under other names. If anyone thinks that I am being unfair to the spirit of John 10, they should read that whole chapter, paying special attention to what Christ says about His sheep. I believe an unbiased appraisal of this passage should begin to get Christians to see that Free-will is not mentioned here at all, and that this is one of the best proofs of God's election.    

Other "whosoever"-type verses that are often quoted are:

"Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God’s one and only Son." (John 3:18)

"He is the atoning sacrifice for our sins, and not only for ours but also for the sins of the whole world." (1st John 2:2)

"And we have seen and testify that the Father has sent his Son to be the Savior of the world." (1st John 4:14)

This first passage (John 3:16 - 18) shows that the one who believes in Christ is not condemned. "Whoever" or "whosoever" is not in the Greek at all. Even if "whoever" was there, it is not the same as "whoever will" (which is Free-will theology in a nutshell), because it implies -something- good in us, in this case "faith", that can commend God's attention toward us in a saving way. "Whoever will", even if it were in these verses in the sense meant by Arminians, is of no help for anyone. You may as well give smelling salts to a corpse. We are dead in sins. We have no good response in us to the good things of God. God has to give us that too. The faith to believe has to be given by God.

I want to answer the other "world" verses, by first quoting a third "world" verse, also from John, and you tell me if there is a contradiction:

"I pray for them. I am not praying for the world, but for those you have given me, for they are yours." (John 17:9)

The same John who tells us here that Jesus is not praying for the whole world has, in the verses above, Jesus dying for the whole world. He is willing to die for everyone, but not pray for everyone? This should be a clue right here that there is a faulty presupposition going on. Which would be harder or more costly to do - to die for someone or to pray for someone?

Because we know that nothing that God does will be thwarted (Romans 9:19 "Who resists His will?") we must understand that for someone to have Christ pay the price for them personally and then reject it, that would be a thwarting of His purpose as far as that individual was concerned. There are many verses that show that God does whatever He wants and succeeds at all that He purposes. His Word will not return to Him void. His death and blood will not have been to any degree wasted or misdirected. Perfect wisdom and sovereign will see to this.

With this in mind, we take a look at 1st John 2:2. Given the verse above and the passage in John 10, we have to reconsider this verse. It is better to say that John was saying that Christ is the "atoning sacrifice for our sins" ("our" meaning John and his hearers/readers), and not only ours but also for the sins of the elect in all the world. This has to be the meaning here or otherwise John contradicts himself.

Unless you are willing to say that it makes sense for Christ to die for everyone - and yet not help everyone to get any Benefit at all out of this dying by His withholding (John 17:9) of the necessary intercessory prayer.