Good question and one where I differ with many Calvinists. I believe the atonement is sufficient for all and offered to all but only the elect respond having been given the gift of faith.
I wrote the following parable as an illustration...
A wealthy man buys ten tickets to Hawaii and has his Son pay cash for them. He sends a letter to ten people with a ticket purchased for them and invites them to join him in Hawaii.
He also sends a Special Courier to deliver three of the tickets to a select group of the ten and has the Courier earnestly persuade them to go {His persuasion is irresistible!} The Courier then escorts them onto the plane insuring they get to Hawaii.
The other seven get the letter and the ticket that has been purchased for them, but because they hate the wealthy man [he makes them feel guilty] they refuse to use the ticket. They each think. If I ever go to Hawaii, I'm going MY way. No one is paying my way, especially not That Guy!
The wealthy man, his son and the courier rejoice with the three in Hawaii. The other seven never make it and their tickets, while paid in full, are never used. While the three are in the beauty of Hawaii with the wealthy man a plague strikes the home towns of the seven and they perish.
NOTE: This is an artificially constructed parable to show how the price can be paid in full for those who refuse to receive the gift. The Father's election and the Spirit's persuasion are limited to the elect, yet a ticket purchased by the Son is legitimately extended to all.
Unlimited Atonement yet Limited Attainment
