I'm talking about the NT. It seems to me that being saved is almost impossible.
First, there's the 'hard' statements by Jesus that counsel plucking out eyes and cutting off things if one even looks or thinks wrong. Then there's the eye of the needle-type statements. Then there's the kind of statements outside the Gospels such as, “If we deliberately keep on sinning after we have received the knowledge of the truth, no sacrifice for sins is left,” (Hebrews 10:26).
You may say the holy spirit will change your heart. Fine. I've heard this answer. Tell it to your Christian neighbors and see if they don't crucify you because I highly doubt that one out of a million have been changed enough to the point where they cease doing things mentioned by Jesus as things they shouldn't be doing ('sinning').
If you can somehow 'save' this religion from being just for the very very very few, I would like to know how you can do it.
Your premise would be false to begin with. Who says you have to "save" Christianity so that it's not just for the very few?
Jesus disagreed with you that such a thing was necessary or even desirable.
And if Jesus disagreed with you, and you want to advocate something different than what Jesus did, then by definition you're not talking about Christianity anymore. Which by definition is a follower of Jesus (Meaning, one who is like Christ. Which is where the ancient term "Christain" comes from in the first place).
Examples where Jesus explicitly tells us to expect that this won't be an easy thing for people to do, and not everyone will make it:
But small is the gate and narrow the road that leads to life, and only a few find it.
Matthew 7:14
Many will say to me on that day, 'Lord, Lord, did we not prophesy in your name and in your name drive out demons and in your name perform many miracles?'
Then I will tell them plainly, 'I never knew you. Away from me, you evildoers!'
Matthew 7:22-23
Again I tell you, it is easier for a camel to go through the eye of a needle than for someone who is rich to enter the kingdom of God."
Matthew 19:24
But the important thing to remember is that Jesus never said it was impossible. He said it was possible. And He put no qualifications on who it was possible for. It's possible for everyone.
When the disciples heard this, they were greatly astonished and asked, "Who then can be saved?"
Jesus looked at them and said, "With man this is impossible, but with God all things are possible."
Matthew 19:25-26
The only qualification is that it must be done with the help of God. Then anyone can do it, because all things are possible with God.
The answer to your question, therefore, is to seek God for the transformation you want. Although, we see elsewhere in Scripture you must seek Him in faith if you expect to get what you're seeking. So make sure you actually have faith in God that He's capable and willing of doing such a thing if you intend to seek Him for such a thing.
Further, I should point out, in response to your title question: The answer is absolutely yes from a pure logic perspective. Logically, the difficulty of doing something has no bearing on whether or not the requirement of you doing that thing is true. That would seem to be a variant of the fallacy of appeal to popularity.
To use an analogy to illustrate; We could say that it's very difficult for most people in the USA to eat healthy and take care of themselves in order to maximize their lifespan and health. But the fact that most people struggle to do this doesn't prevent it from being true to say that if they don't do it they will die younger than they should have and you'll develop illnesses you otherwise wouldn't have.
Likewise, there's logically nothing contradictory with saying it's true that you must do what Jesus said in order to experience salvation, but also say it's true that most people won't be willing or able to do that. The difficulty of a task does not necessarily have any connection to proving whether or not said task is necessary. If logic worked that way, then eating perfectly healthy and taking care of your body in other ways would be completely unnecessary and have no benefit to you because most people aren't willing to do it.