The first thing that strikes me in this teaching is its parallel in Luke. Replying to the question, "Lord, will only a few be saved?" Jesus says "Strive to enter through the narrow door, for many, I tell you, will try to enter and will not be able." (Luke 13: 23-24). While you are right to preempt any notion that Jesus is saying only Christians can be saved (after all there was no Christianity when Jesus taught), he does seem to be saying that most of humanity will be damned.
Why is salvation so difficult? When I ponder this question I cannot come up with a satisfactory answer. At least not as long as I posit a God who consciously set up a system of salvation. Why would God make it so hard to find him? Why not make the gate to God as wide as possible? Doesn't God want us to come to him? This would be the message of the Prodigal Son, at least as I read the parable. Has Jesus changed his mind?
I can imagine a system of salvation in which people can opt out. If someone decides they prefer hell to heaven, fine. But why set it up so that most who desire heaven are denied entry?
In Pure Land Buddhism, Amida Buddha, the Buddha of Infinite Light, puts off his own salvation until he has facilitated the salvation of all sentient beings. All you have to do to get his help is call his name. Sure most people try to make it on their own, but when they finally realize they can't succeed they sincerely call for help, and Amida is there. This seems much more Christ-like than Jesus' notion that "the owner of the house [who I assume is God] has got up and shut the door" (Luke 13:25) leaving millions clamoring to get in. Where is the love and compassion in that?
It seems to me that a loving God would make finding Him easy, and that it is only us humans that imagine the way to be hard. Which leads me to Franz Kafka's parable of The Law. In this parable Kafka imagines a man who finds the gate to the Law (God) but fears to enter because the gate is guarded by a giant. The man spends his entire life trying to bribe the giant to let him in, but the giant never grants him entry. At the end of his life he asks the giant to explain why no one else has ever come to the gate. The giant explains that this gate was for him alone. No permission to enter was every needed. All he had to do was walk through it.
In other words, the narrow gate is the gate made just for you. It is narrow because only you can fit through it. It isn't narrow to keep people out, for each person has her own gate. The challenge is to find our gate and walk through it. What is our gate? It is this very moment; it is whatever life asks of us here and now. If we engage this moment loving God, neighbor, self, and stranger then we enter the gate. If we engage the moment with something other than love (and I would say compassion are justice are the two ways of love) then we do not enter the gate. The choice is ours.
In this way of understanding salvation, the way to God is universal. Each person has her or his own gate. There is no attempt to keep people out. True, you have to find your gate and walk through it, but it is right there in front of you. Walk on!