How to get to heaven, according to Jesus

So I've been listening to this Christian radio channel regularly for a few weeks now, and every Sunday, they have this program where they dissect a small segment of the Bible, analyzing and interpreting it. (I had thought that Christians should just accept the Bible as it is without trying to read into it too much. I mean, isn't religion supposed to be about blind faith, not reasoning?)

Anyway, I recently heard one of these programs. They were talking about the part of the book where Jesus takes the "sheep" with him to eternal life and leaves the "goats" to rot in hell, more or less. The verdict of the analysis panel was that you can't earn your spot in heaven by doing good things as a means to get to heaven; you have to do them selflessly. In a Kantian way, if you get even the smallest amount of feel-good to yourself from, say, giving money to charity, you won't get to heaven.

What the hell?! Wouldn't that mean that absolutely no one, safe for Jesus, gets to heaven?

I have no idea how Christians can have faith in the promise of salvation when the Bible seems to alternate between promising eternal life to everyone who believes, and then promising eternal life only to those few who have somehow guessed the right way to earn it.

Thank God I'm not a Christian, nor desirous of eternal life.