Calvinists can point to many verses in Scripture that would support their view that humanity is totally depraved.  Here’s a sampling:

Jeremiah 17:9 The heart is deceitful above all things, and desperately corrupt; who can understand it?

Mark 7:21-23 For from within, out of the heart of man, come evil thoughts, fornication, theft, murder, adultery, coveting, wickedness, deceit, licentiousness, envy, slander, pride, foolishness.  All these evil things come from within, and they defile a man.

John 3:19 And this is the judgment, that the light has come into the world, and men loved darkness rather than light, because their deeds were evil.

Ephesians 4:18 they are darkened in their understanding, alienated from the life of God because of the ignorance that is in them, due to their hardness of heart

2 Corinthians 4:3-4 And even if our gospel is veiled, it is veiled only to those who are perishing.  In their case the god of this world has blinded the minds of the unbelievers, to keep them from seeing the light of the gospel of the glory of Christ, who is the likeness of God.

Romans 3:9-12 What then?  Are we Jews any better off?  No, not at all; for I have already charged that all men, both Jews and Greeks, are under the power of sin, as it is written: “None is righteous, no, not one; no one understands, no one seeks for God.  All have turned aside, together they have gone wrong; no one does good, not even one.”

There is also a view in Calvinism that even if someone who is not one of the “elect” performs a charitable act, God still sees this as sinful.  From the Westminster Statement of Faith:

“Works done by unregenerate men, although for the matter of them they may be things which God commands; and of good use both to themselves and others: yet, because they proceed not from an heart purified by faith; nor are done in a right manner, according to the Word; nor to a right end, the glory of God, they are therefore sinful, and cannot please God, or make a man meet to receive grace from God: and yet, their neglect of them is more sinful and displeasing unto God.”

Non-Calvinists will often counter total depravity by pointing out that even while St. Paul writes in Romans that all are under the power of sin and that “none is righteous” Scripture gives us multiple examples of people who are indeed righteous.  If we go back to the story of Cain and Abel in Genesis 4, we see that God accepted the offering of Abel but rejected the offering of Cain, because Abel brought the best of what was his and Cain did not.  In these first early brothers we do not see two men who are both incapable of pleasing God.  We also see that God warns Cain that “…sin is couching at the door; its desire is for you, but you must master it.”  (Genesis 4:7).  He indicates to Cain that while the tendency to sin is indeed strong within him, he has the ability to fight it.  Cain chooses not to.

The Old Testament has a multitude of people that walked with God and were considered by God to be righteous — Enoch, Noah, Abraham, Joseph, Moses, King David to name a few.  Calvinists would claim this is because they walked by faith in the promise of a Savior.

But then we come to the New Testament, and we see a perfect illustration of an unregenerate man who has found favor with God.  In Acts Chapter 10 we meet Cornelius.  Cornelius is a Gentile man who has not yet become a Christian.  But Scripture refers to him as “a devout man who feared God with all his household, gave alms liberally to the people, and prayed constantly to God (v2).”  And the angel who visits him tells him that “Your prayers and your alms have ascended as a memorial before God(v4).”  Far from seeing his acts as sinful, God recognizes the goodness in his heart, and this is before he becomes born again.

In more recent history we can look to those the Jewish people have given the honor of the “Righteous Among the Nations” for their willingness to risk their own careers, livelihood, lives and often the lives of their families to save Jews during the Holocaust.  Counted among their number are an a professed atheist, a Deist and 43 Muslims.  Only God can be the judge of these people and their eternal destiny, but as a Catholic I would firmly reject the idea that their willingness to sacrifice themselves to save others would be seen by God as sinful and not pleasing to Him.  For as Christ said, “Greater love has no man than this, that a man lay down his life for his friends.”  (John 15:13).