Hello, I am going to jump in here now with a different view. I believe it was and is possible to keep the law. Now when I say law, and most of the time when the Biblical writers refer to the law, they are referring to the law of Moses as contained in the first five books of the Bible. I don't want to quibble about exceptions, I know there are some. But most of the time that is the law they are talking about. So how can I say that it is possible to keep the law?
First of all, Deuteronomy 30:11 says that "Now what I am commanding you today is not too difficult for you or beyond your reach." Also, it is said of Hezekiah the king in 2 Kings 18:6: "He held fast to the Lord and did not cease to follow him; he kept the commands the Lord had given to Moses." And it is said of Zechariah and Elizabeth in Luke 1:6 that: "Both of them were upright in the sight of God, observing all the Lord's commandments and regulations blamelessly."
Now you may say, how is that possible? Everybody sins. That is true. Even Hezekiah, Zechariah, and Elizabeth sinned. However, we need to understand the way the Bible speaks about someone who keeps the law, or about someone who obeys the law. You see, the law of Moses was not simply a list of laws or rules, but contained within itself a way for sin to be forgiven. In other words, God expected that those who kept and obeyed the law would sin, and so, within the law itself, provided a way for atonement in the form of sacrifices. These sacrifices prefigured, were based on, and ultimately derived their power from the death of Christ on the cross.
So then, "keeping the law" or "obeying the commandments" in the Bible did not refer to those who were sinless, rather to those who trusted in God and determined to live their lives in obedience to him. By God's grace they followed him, and when they sinned, they repented and trusted in God's provision for atonement. We know that Hezekiah sinned in arrogance and foolishness. And yet, when summarizing his life, the Biblical writer says that on the whole, Hezekiah kept the commands the Lord had commanded Moses.
Thus, I think that asking the question is a misunderstanding of the way the Bible uses language, of the way the law worked in the Old Testament, and of how it can work today.