The strait gate and narrow road story is far from the only passage in the Lord's teaching that points to salvation being a journey it was just the most obviously journey-related because it speaks of a road that leads to eternal life. The other passages are the ones where he speaks of the arduous work and faithful obedience that yield the fruit of salvation.
Jesus answered them and said, Verily, verily, I say unto you, Ye seek me, not because ye saw the miracles, but because ye did eat of the loaves, and were filled. Labour not for the meat which perisheth, but for that meat which endureth unto everlasting life, which the Son of man shall give unto you: for him hath God the Father sealed.
John 6:26-27
I am the true vine, and my Father is the husbandman. Every branch in me that beareth not fruit he taketh away: and every branch that beareth fruit, he purgeth it, that it may bring forth more fruit. Now ye are clean through the word which I have spoken unto you. Abide in me, and I in you. As the branch cannot bear fruit of itself, except it abide in the vine; no more can ye, except ye abide in me. I am the vine, ye are the branches: He that abideth in me, and I in him, the same bringeth forth much fruit: for without me ye can do nothing. If a man abide not in me, he is cast forth as a branch, and is withered; and men gather them, and cast them into the fire, and they are burned. If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you. Herein is my Father glorified, that ye bear much fruit; so shall ye be my disciples. As the Father hath loved me, so have I loved you: continue ye in my love. If ye keep my commandments, ye shall abide in my love; even as I have kept my Father's commandments, and abide in his love.
John 15:1-10
There are other passages too, you can probably think of some yourself, and there are the comments of saint Paul about running the race so as to receive the prize and not be disqualified.
PS: none of what I've said and none of what I believe means that one is not saved solely because of the grace of God and the saving work of Jesus Christ. I am inclined to say this:
- a person cannot know with absolute certainty that they are 'saved' but they can be confident in God's promises and that counts for a lot.
- only God knows absolutely who is saved and who will be saved and who was saved. It's one of the attributes of deity to know everything that can be known.
- human beings who want to claim absolute knowledge of their own salvation ought to take the warnings from the new testament seriously including the one from Hebrews that I quoted in an earlier post.