While there is not a Bible verse that specifically states we commit a sinful act each day, we do have verses that remind us that we have inherited the capacity to sin at any moment. "Sin entered the world through one man, and death through sin, and in this way death came to all men, because all sinned" (Romans 5:12). "Surely I was sinful at birth, sinful from the time my mother conceived me" (Psalm 51:5). In addition, we have commands that we know we never keep, much less on a daily basis. For instance, who can claim to love God with all his heart, mind and soul every moment of every day? No one. Yet, that is the greatest commandment (Matthew 22:36-38). Failing to love God completely at all times is a daily sin for all Christians.
We also have a verse that warns us of the deceitfulness of our old sinful nature, which in a sense is warning us of the potential, if not the likelihood, of daily sin. "The heart is deceitful above all things, and desperately wicked: who can know it?" (Jeremiah 17:9). Even the apostle Paul was frustrated with his own battle against indwelling sin. "For I delight in the law of God after the inward man: But I see another law in my members, warring against the law of my mind, and bringing me into captivity to the law of sin which is in my members" (Romans 7:22-23). This capacity to sin led him to cry in desperation, "What a wretched man I am! Who will rescue me from this body of death?" (Romans 7:24).
Solomon knew full well that he and all men not only have the potential for sin, but that we all exercise that capacity routinely. As he stated in his prayer at the dedication of the temple, "If they sin against you—for there is no one who does not sin…" (1 Kings 8:46). And Solomon spoke of it again in the book of Ecclesiastes: "Surely there is not a righteous man on earth who does good and never sins" (Ecclesiastes 7:20). Again, while these verses do not unequivocally indicate daily sin, they certainly warn us against the pride of saying at any moment that we have no sin.
The good news is that we will not have to strive forever against daily sin. One day we will be in heaven with our Savior and will be freed from the presence and power of sin, just as we have already been freed from its penalty.