Relatively speaking, the answer is "yes".
The support for this answer can be found in many places in scripture but for today, let's take a look at Luke 13:22-28.
It is here that someone asked Jesus this question: “Lord, are only a few people going to be saved?”. This was Jesus' response to that person:
“Make every effort to enter through the narrow door, because many, I tell you, will try to enter and will not be able to. Once the owner of the house gets up and closes the door, you will stand outside knocking and pleading, ‘Sir, open the door for us.’
“But he will answer, ‘I don’t know you or where you come from.’
“Then you will say, ‘We ate and drank with you, and you taught in our streets.’
“But he will reply, ‘I don’t know you or where you come from. Away from me, all you evildoers!’
This is an amazing passage to unpack. There are two important truths I would like to unpack here. One, I would like to talk about this narrow door, and two, I would like to talk about who the owner of this house is in this passage.
First we see that in answering this question, Jesus made it clear that there is in fact a narrow door in which people are being saved by. What did Jesus mean by saying that the door was narrow?
Well, we can look at other passages in scripture to give us some incite. In John 10:9, Jesus says, "I am the door. If anyone enters by Me, he will be saved and will go in and out and find pasture". So here, Jesus is defining the door as Himself. By being a narrow door Jesus presents a very specific way, and by a very specific means, by which a man or woman shall be saved. It is through Jesus Himself. In Matt 7:13-14, Jesus says “Enter by the narrow gate. For the gate is wide and the way is easy that leads to destruction, and those who enter by it are many. For the gate is narrow and the way is hard that leads to life, and those who find it are few." So it is pretty clear here that not many people will choose Jesus who in choosing Him is synonymous with choosing life. Finally, in John 14:6, Jesus says “I am the way, and the truth, and the life. No one comes to the Father except through me." Here Jesus makes it even more clear that He is not only the way, or the door, but He is also the ultimate truth and the ultimate life. If we come to Jesus we find the path to salvation, the path to ultimate truth, and the path to eternal life. Many non-Christians, and even some Christians, struggle with the fact that Jesus defines Himself as the only way to salvation. Some Christians are called narrow minded because they embrace Jesus words in the scripture. My encouragement to these people is always the same: You can't say, "well there are so many religions to choose from" but then get mad when Christ has clearly made Christianity so distinct, and so specific from all religions, that it can be called narrowly specific. It is the most clearly defined path to salvation. There is no doubt that this is a very specific path in which God is speaking of which man should be saved and man must "make every effort" to be trusting that this is the case in order to be saved. The only alternative to Jesus is to try some other way, which is not the way, not the truth, or not life. This alternative will end in weeping and gnashing of teeth and Jesus proclaiming to the person "depart from Me".
I just briefly want to touch on the second point. That is, who is the owner of this house that Jesus speaks of in Luke 13:25?
It always fascinates me on how many ways Jesus claims to be God in scripture. This way is not an exception. In Luke 13:25 it says "When once the master of the house has risen and shut the door". We know who the door is in this and other passages. The door is Jesus, the way is Jesus, but if we keep reading, we see that the Master of this house is Jesus too! How can we know that? Jesus explains what the people who are shut out says to the Master of the house when they are shut out in Luke 13:26 "We ate and drank in your presence, and you taught in our streets.’ When did people eat and drink in the presence of this Master? When did He teach in their streets? This Master was and is of course none other than Jesus Christ Himself. He is the person who ultimately decides our fate if we do, or do not, decide to trust Him as the narrow way.
In conclusion, it is clear that Jesus defines the way to salvation as being a very hard, a very narrow, and a very thing that many will not choose. However, this shouldn't stop us from proclaiming the narrow way.