What I believe from my understanding of the Bible is compared to a perfectly holy God, we do all fall short or miss the mark of perfect holiness. Not one human being can claim that, yet that is what is required by God to enter Heaven. Here are a couple verses: (I underlined the emphasized words so you don't have to read all of it)
for if there had been a law given which could have given life, verily righteousness should have been by the law. 22But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe. Galatians 3:21b-22
For all have sinned, and come short of the glory of God; Romans 3:22-24
Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned: Romans 5:11-13
Therefore as by the offense of one judgment came upon all men to condemnation; even so by the righteousness of one the free gift came upon all men unto justification of life. Romans 5:17-19
This is just what I believe. I believe these verses are true and that all have sinned. I know for sure that I have. I sin every single day many times over. I believe we need a righteousness not of our own. I believe when we trust Christ to have paid the penalty for our sin and he gives us the free gift of eternal life, he also gives us his righteousness in place of our own. So I believe our sins are all paid for and we have Christ's robe of righteousness on and God sees us as holy and blameless, not because of what we have done, but because of what Christ has done. I believe this way, everyone can be saved who wants to and nobody can boast except in the cross of Christ.