A friend tweeted the YouVersion verse of the day this morning. She tweeted it from the New Living Translation. Something didn’t seem quite right about it, so I decided to compare it to some other popular translations. See what you think.
And, the text of those, in case the image is not viewable for some.
Matthew 6:33
From the New International Version: 33 But seek first his kingdom and his righteousness, and all these things will be given to you as well.
From the King James Version: 33 But seek ye first the kingdom of God, and his righteousness; and all these things shall be added unto you.
From the English Standard Version: 33 But seek first the kingdom of God and his righteousness,and all these things will be added to you.
From the New Living Translation: 33 Seek the Kingdom of God[a] above all else, and live righteously, and he will give you everything you need.
There is a huge difference between seeking God’s righteousness and living righteously. We need salvation because we don’t and can’t live righteously. The Pharisees thought they could live righteously, and much of the sermon on the mount was to prove that even they can’t do it.
I don’t know Greek yet, but I see considerable differences in the translations here. I’m far from infallible, and admit I could be wrong, but these seem very different to me.

I'm not so sure your next-to-last paragraph is really disagreeing with the NLT editors here. After all, the more literal translations also say in Matthew 5 to "be perfect, as your heavenly Father is perfect." In 6:33, there are really a few different options for how Jesus would say "seek…his righteousness" in modern English, and "live righteously" may actually be really close to the best one.
The issue here is the big issue with all phrase-for-phrase translations, in that they remove the ambiguities of the original to provide their own interpretation of a verse, which may or may not be correct. The word-for-word translations leave the ambiguity in ("seek his righteousness" has little if any concrete meaning) and allow the local pastor/teacher/reader/learner to have access to the original and interpret for themselves. At least, that's their basic philosophy, though they may in practice deviate often.
I don't think "seek His righteousness" is ambiguous. It seems to me to be a clear Gospel passage. We seek Christ's righteousness. That is, we seek the righteousness that is imputed to believers. "Live righteously" is a law command, similar to the two greatest commandments in Matthew 12. Jesus would be teaching the Pharisee's teaching if the case was to "live righteously."
What about Matthew 6:14? Is this a 'gospel passage': If you forgive others their trespasses, your heavenly father will also forgive you. What about 6:18: …your Father who sees in secret will reward you. 7:7? Ask and it will be given to you.
I understand the desire to see imputed righteousness here, but I don't think you don't have to make Matthew's logical progression identical to Paul's. Matthew strongly portrays Jesus as greater than the Pharisees, even greater than the original lawholder/giver Moses. To do so, he presents the law of Jesus as being even beyond the law God gave to Moses, and I believe Matthew is patient in allowing the reader to come to his own conclusion that all men are incapable of fulfilling this law apart from the final act of the Gospel, Jesus' death and resurrection (the theme of Messiah is present throughout, but substitution is not made explicit until 20:28).
After reading this post I have to say that, unfortunately, you do not understand the phrase, "and his righteousness." You've made a mountain out of this misunderstanding. The Lord Jesus is not introducing a new subject of imputed righteousness -- let alone a "works righteousness," but he is speaking of the ethical, righteous lifestyle that God requires of his disciples.
In fact, D.A. Carson has articulated quite well the consensus of nearly 10 different commentaries I consulted on that phrase saying,
"To seek God's righteousness is not, in this context, to seek justification. "Righteousness" must be interpreted as in 5:6, 10, 20; 6:1. It is to pursue righteousness of life in full submission to the will of God, as prescribed by Jesus throughout this discourse."
Again, this understanding is indicative of the thought of every commentator I've read from Broadus, to R.T. France, to Leon Morris, to Turner, Nolland and Hendriksen, etc. Considering that Jesus is in the midst of the Sermon on the Mount, what he is saying, contra to the worry and anxiety of the immediately preceding context is to seek God's rule (his kingdom) and his righteousness (the righteous way of living).
In reality the NLT has a measure of (correct) interpretation in the translation. But is does not in any way suggest a "works righteousness." And this translation is not at all a reason to not use the translation, IMO.
I've done some revising to this, taking in mind some comments, here and those I saw on Facebook. While I still believe this is a Gospel passage, saying we should seek first gifted righteousness, I did remove some of the things I said regarding the NLT. I still think it is a poor translation of this passage, and a poor translation in general.
I certainly do appreciate your teachable spirit and willingness to revise your post. It shows great character. And though I wouldn't die on this hill, the passage -- from the context of the Sermon on the Mount as well as Matthew's usage of "righteousness" -- leaves very little ambiguity as to whether or not he's speaking of imputed righteousness -- a concept totally foreign to the context of this discourse or an ethical righteousness as one walks in the way of God. That is why almost unanimously all commentators (except a few older commentators like Gill who tend to be more myopic and doctrinal rather than expositional) see it this way. Regardless, may the Lord bless your study!
This is not a poor translation of the passage. I grant you that the Greek is phrased in the same way as the other translations. I don't know why the translators of the NLT translated it this way. Variety
This is not a poor translation of the passage. I grant you that the Greek is phrased in the same way as the other translations. I don't know why the translators of the NLT translated it this way. Variety perhaps? But it is not in any way teaching works righteousness!
And how is it a "gospel passage"? Because you say so?
I’m the top hit on Google for “calvinist righteous lifestyle.” http://t.co/lRQe0qMa I don’t know if that is a good thing or a bad thing.