"Will only a few be saved?" I think the fact that Jesus does not answer this question directly is the first clue that it's probably the wrong question, or perhaps that Jesus detects a wrong motivation behind the question.
At first, it seems like he is supporting an exclusivist view of salvation. The door is narrow; strive to enter the narrow door. The question is already being turned against its askers with the implied subject of the imperative: "You strive for the narrow door." What was their motivation in asking? Will we be among the lucky ones who are included? Will the people that annoy us be excluded so that we can can triumph over them? Jesus corrects this line of thought with "You worry about yourself."
Knowing Jesus is not enough: "We ate and drank with you, and you taught in our streets." The image here is that you might get stuck on the wrong side of the door. The problem is not so much a narrow door as a narrow time to enter it. Be sure in your striving that you 're on the right side of the door. What is the right side of the door? Relationship with the owner of the house. The parable turns at the weeping and gnashing of the teeth. If we must speak in terms of a cosmic setting, this invokes the images of hell which, for us modern people, includes way too much Dante and not enough Bible.
Some will be surprised to see Jewish people there: Abraham, Isaac, Jacob and the prophets. Perhaps in Luke's time, the Christians were starting to reject the Jews, or rather to accuse the Jews of rejecting Jesus. What a surprise to see them on the inside, and the insiders stuck on the wrong side of the door. Actually, it shifts from the passive being stuck to a more active image: being thrown out. In Greek, that word for being thrown out, εκβαλλω / ekballo, is also used in demon exorcism stories. The demon is "ekballo'd" from the person possessed. It's probably making too much of this coincidence, but to my ear, I hear the exclusivist askers being accused of being demons that will be exorcised from relationship with the owner of the house. Slightly less cosmic, the story of the man born blind uses ekballo to describe being thrown out of the community, so maybe the exclusivist askers will be exorcised by being ejected from the communal relationships in the long run.
The really interesting thing is that "people will come from the east and the west and the north and the south to be in the kingdom of God." This brings to my mind radical inclusion images from Isaiah. It talks about people from all lands coming to Jerusalem to worship God. What started out as an exclusivist image of a narrow door has become an inclusivist image. "Will only a few be saved?" It sounds like the final answer is that many will be saved, but that the ones asking this question should check their motivations. They should not worry about others, not judge, not exclude, but should check themselves and stay in relation with the God and savior who can and will save many, lest they get stuck on the wrong side of the door.