Satyagraha, like kpickell, I'm a bit skeptical of looking just at the Torah (Genesis through Deuteronomy) as the whole of the "Word of God" that Christians claim to follow. You'd have to look at the entirety of the scriptures that Christians claim.
While certain Jewish patriarchs and kings had multiple wives and concubines--thereby not falling under the "sleeping only with one spouse" standard set forth today--it's important to note that all ancient cultures to my knowlege viewed women as property, so having more than one was a sign of wealth. Sticking only to your spouse(s) for sexual matters was valued, though, as can clearly be seen in Song of Songs.
As far as New Testament references that clearly condemn sexual behavior outside of marriage, Hebrews 13:4 does a nice job of that. Marriage should be honored by all, and the marriage bed kept pure, for God will judge the adulterer and all the sexually immoral.
Also, Christian theology teaches that marriage is supposed to be a picture of God's love for Israel and/or the Church. Adultery is often compared to idolotry, as idolotry is "cheating on God". II Corinthians 11:2
talks about the Church being presented as a 'pure virgin' to Christ in the end. Now, obviously people are not pure and virginal, but that's why there's also a theology of grace and redemption so the Church can be considered a pure virgin again.
Anyway, what I was trying to say is that Christians do reasonably infer from their scriptures that they ought not have sex outside of marriage.
And, now you know two Christians who aren't "playing around", as you put it. I didn't engage in any kind sexual intercourse when I was a teenager, and at a single 22, I still don't. Granted, I was pretty sheltered growing up, but your assertion was that it was unrealistic for anyone in any situation to refrain from sexual contact.