Righteous Dude

The adversary is clever. He takes something true and twists it. When ever I am discussing the applicability of the Law of God with other believers, one thing that almost always comes up is the idea of "My works being my righteousness" and "seeking to establish my own righteousness".  One of the verses that might even get thrown my way when I am talking about being obedient to the Law of God is this one:

For not knowing about God’s righteousness and seeking to establish their own, they did not subject themselves to the righteousness of God..- Romans 10

That right there is the adversarial twist... that somehow by doing exactly what the Messiah said and told us to do, is establishing our own Righteousness. What this does is dismisses the fact that God Himself is the one that sets the standard of what IS righteous. When we read in Deuteronomy 6:

So the Lord commanded us to observe all these statutes, to fear the Lord our God for our good always and for our survival, as it is today. 25 It will be righteousness for us if we are careful to observe all this commandment before the Lord our God, just as He commanded us.

According to this verse, When we are obedient to HIS commands, we are walking in HIS Righteousness, as it is also written that the submitting to the commands of God is hostility to the flesh:

For the mind set on the flesh is death, but the mind set on the Spirit is life and peace, 7 because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able to do so, 8 and those who are in the flesh cannot please God.- Romans 8

If by faith in Christ, you are doing the deeds of Christ, you're walking in HIS righteousness, as a response to your salvation.  IF you are following the Law for any other reason, you're seeking to establish your own righteousness and you've lost the plot. Look at this:

What does it profit, my brethren, if someone says he has faith but does not have works? Can faith save him? 15 If a brother or sister is naked and destitute of daily food, 16 and one of you says to them, “Depart in peace, be warmed and filled,” but you do not give them the things which are needed for the body, what does it profit? 17 Thus also faith by itself, if it does not have works, is dead.
18 But someone will say, “You have faith, and I have works.” Show me your faith without your works, and I will show you my faith by my works. - James 2 

What this is saying over and over again is that your faith should result in doing the commands of God, which by your faith shall be credited to you as righteousness. If you're of the mindset that "God saved me, now I just get to sit here and do nothing" I'd point you to the parable of the  talents.