From what I understand about modern evangelicalism is that, in those churches, typically, only adults (or those who have come to what I'll call a "mature faith") are baptized because it's representative (that is, not required for salvation) of the new life they have committed to following God. Since babies cannot make that commitment, they do not baptize babies. Additionally, after the ascension of Jesus there is no record of babies/infants/toddlers being baptized by the apostles. Instead, adults were only baptized by immersion after they had demonstrated saving faith in Christ.
When it comes to issues with literal interpretations of John 3 (water and the spirit), there are answers to be had, though I won't speak as to whether they are convincing. Ezekiel 36 speaks of the promise of the New Covenant and promises a cleansing water for those under it (as a Pharisee, it is highly likely that Nicodemus had memorized Ezekiel's prophecies, and certainly knew of them). John 7 refers to the Holy Spirit within believers as living water. Though it may simply state the obvious, we do appear to come from a sack of water at birth.
As far as whether an unbaptized infant (or even a stillborn or miscarried child) is denied heaven, I suppose that depends on who you talk to. Most of my friends in the evangelical community appeal to the goodness of God and his demonstrable affection for children in the Bible in believing that babies who have no concept of God are admitted into paradise.