To answer this question, we must first understand a few things. First of all, we must understand that God's standard for goodness is not the same as ours. As humans, when we judge our own goodness, we do it by comparing ourselves with other people. Of course, an average person will look so good when compared to illegal drug peddlers, rapists, murderers, etc. But we must understand that come Judgment Day, our goodness will not be compared to other people. We will be compared to God's holiness. The Bible instructs us to be holy as God (1 Peter 1:15-16), and Matthew 5:48 tells us that God is perfect. Now that's a big problem to be compared to God.
But the problem gets even bigger! The Bible tells us that there is no one person that has ever lived that is "good" on God's standard (Romans 3:10, 23). And actually, we do know that as we all have lied, stolen things, looked with lust at someone (equal to adultery in God's sight), hated someone (equal to murder in God's sight), dishonored our parents, rendered worship to gods of our own making, blasphemed God, coveted things others possess, failed many times to give one day of a week to God and deprived God of first place in our lives. So the question should not be, "Am I good enough to get to Heaven?" Instead, we should be asking "How bad have I been in God's sight?" And because we are to be compared to God's goodness on Judgment Day, the answer to the second question is "very bad!"
This now means that no matter how much we try to be good on our own; even if you give every bit of your wealth to charity, engage in every religious rite, we will never ever be as good as God. We will always be disqualified for Heaven for we have already sinned against God. Our rightful place will always be in Hell (Romans 6:23).
So is there really no hope for us anymore? Thank God, He made hope possible through Jesus Christ. When God's Son came to earth, He did what we failed to do, and that is He fulfilled the Law (Matthew 5:17). He did this by living a perfect life. Not even the great tempter, Satan, with all of his worldly offers could make Jesus give in to sin (Matthew 4:1-11). 1 John 3:5 affirms that Jesus lived a sinless life in all of his 33 years here. Then, despite the perfect life He lived, Jesus died a cruel criminal's death by dying on the cross. Why did He allow Himself to go through this humiliating ordeal? 2 Corinthians 5:21 gives us the answer: "For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." By dying a sinful person's death despite having no sin, He can change places with us. Give your sins to Him and let them be crucified with Christ at the cross. Jesus, in turn, gives His perfection to you which is what 2 Corinthians 5:21 is implying when it states, "that we might be made the righteousness of God in him."
Jesus Christ already did all the paying for us. All we need to do is to repent of our sins (turn away from them) and put our complete trust (faith) on Him for our salvation. As a result, Jesus' goodness will be transferred to us, making us so qualified of Heaven now.
So the answer to the question of this article is "No, we cannot be good enough for Heaven on our own, but through Jesus, we will be so fit to be with Him in His Kingdom!"