Jesus, But Perhaps Not You, May Or May Not Save

Will someone please tell me on what part of the New Testament missionaries and proselytization is based and what people have interpreted this to mean?

I've always wondered, from the days the missionaries first got their claws into me in Africa 'til last week when two guys came by asking if anyone in the house spoke Spanish, so they could read the Bible with them. Saw two very very way too pink young Mormons trudging alongside the highway in the desert with gigantic backpacks, spindly bicycles, and their pinkening scalps showing through the white-blonde buzz cuts.

I have been moved to ask this question by auntysocial's amazing JESUS SAVES pix and post.