Those Whose Walk Is Blameless

For the Lord God is a sun and shield; the Lord bestows favor and honor; no good thing does he withhold from those whose walk is blameless. (Psalms 84:11)
"Those whose walk is blameless." Is it possible to have a blameless walk with Christ? It most certainly is, just as it was under the Law of Moses.
Somehow there has crept into Christian thinking that no one can live perfectly before God. You will hear Christians say, "As long as we are in the world we have to sin."
Where do they get this idea—that we have to sin while we are in the world; that it is impossible to have a blameless walk?
Even under the Law of Moses it was possible to please God perfectly:
In the time of Herod king of Judea there was a priest named Zechariah, who belonged to the priestly division of Abijah; his wife Elizabeth was also a descendant of Aaron. Both of them were upright in the sight of God, observing all the Lord’s commandments and regulations blamelessly. (Lule 1:5,6)
Consider the passage above: Zechariah and Elizabeth were living under the Law of Moses. Were they blameless before God? If they were, if they satisfied the requirements of Psalm 84:11, then how can we say that it is impossible to live without sin? If Zechariah and Elizabeth were under the Law of Moses, observing all the Lord's commandments and regulations blamelessly, then what could be true of us under a vastly superior covenant?
But you might say, "They kept the Law perfectly, but they themselves still were not as perfect as Christ." That certainly is true. But God does not require that we live perfectly beyond what He is requiring of us at any given time. This may be true for eternity, as far as I know.