One of the clearest passages in scripture teaching Christ came to save each and every person is John 12:46-48:
I have come as a light into the world, that whoever believes in Me should not abide in darkness. And if anyone hears My words and does not believe, I do not judge him; for I did not come to judge the world but to save the world. He who rejects Me, and does not receive My words, has that which judges him—the word that I have spoken will judge him in the last day.
Notice a few things about world. First, Christ comes “into” the world. You go into a place, in this case Christ went into the planet earth. And who on earth will be judged one day? Each and every person who ever lived on earth. So who did Christ come to save? Every person who has ever lived on the earth, including those who rejected Him and will be judged on the last day. One of the key issues in the limited/unlimited atonement debate is God’s intention, plan and design in sending Christ into the world and according to Christ, He came to save the world. This isn’t some overly simple all means all folks- we have strong reason to believe in unlimited atonement.