When I was very young, I was taught that rich people could not get into heaven because they were too caught up in their riches to care about God. When I was older, I learned that it is being rich toward oneself instead of being rich toward God that distances a person from God. Now I've made an observation that, now that I see it, seems obvious, and others have probably already made the same observation.

“And, behold, one came and said unto him, Good Master, what good thing shall I do, that I may have eternal life? And he said unto him, Why callest thou me good? [there is] none good but one, [that is], God: but if thou wilt enter into life, keep the commandments. He saith unto him, Which? Jesus said, Thou shalt do no murder, Thou shalt not commit adultery, Thou shalt not steal, Thou shalt not bear false witness, Honour thy father and [thy] mother: and, Thou shalt love thy neighbour as thyself. The young man saith unto him, All these things have I kept from my youth up: what lack I yet? Jesus said unto him, If thou wilt be perfect, go [and] sell that thou hast, and give to the poor, and thou shalt have treasure in heaven: and come [and] follow me. But when the young man heard that saying, he went away sorrowful: for he had great possessions. Then said Jesus unto his disciples, Verily I say unto you, That a rich man shall hardly enter into the kingdom of heaven. And again I say unto you, It is easier for a camel to go through the eye of a needle, than for a rich man to enter into the kingdom of God. When his disciples heard [it], they were exceedingly amazed, saying, Who then can be saved? But Jesus beheld [them], and said unto them, With men this is impossible; but with God all things are possible.” (Matthew 19:16-26 AV)

Christ is not only saying that it is highly unlikely that someone who has the riches of self-righteousness will enter into the kingdom of
God.

1 Corinthians 1:26 For ye see your calling, brethren, how that not many wise men after the flesh, not many mighty, not many noble, [are called]:

He is also saying that, while it is highly unlikely, it is not impossible. God is able to save even the pharisee or the sadducee. Just look at what He did for Paul, a man who was killing Christians, including ordering the death of Stephen.

Matthew 5:3 ¶ Blessed [are] the poor in spirit: for theirs is the kingdom of heaven.

Paulwas rich in spirit until God took him and made him poor in spirit. He can do that with anyone He chooses. Even someone who is spiritually proud, even someone who appears unsavable, the "rich" of this world. With God, all things are possible.