These are widely recognized as the theme verses of Paul's letter to the church at Rome. They are the thesis of what turns out to be one very long, sustained argument. As a result, there is a lot to unpack here. (After all, Paul will spend the rest of the letter doing just that.) But it is those final words, the quotation from Habakkuk 2:4 which I find most interesting and most enlightening for understanding these verses and the whole of Romans.
Habakkuk is a little prophetic book that begins with a familiar question:
"O Lord, how long shall I cry for help and you will not hear? Or cry to you "Violence!" and you will not save?"The first four verses of Habakkuk paint a bleak picture of Israel as a violent and unjust place. Habakkuk says that the law is "paralyzed" and "justice goes forth perverted." This is an especially poignant depiction of corruption given that the law to which Habakkuk refers is the good and perfect law given by God. The corruption and injustice in Israel are so severe that even God's perfect law is powerless to correct it. The overwhelming sin of Israel perverts the instrument of God's own justice so badly that it only serves to produce more injustice. It is this dismal circumstance which causes the prophet to cry out to God asking "How long?".
To say that God's response to Habakkuk in 1:5-11 would have been "surprising" or "unexpected" would be an understatement overwhelming in its imprecision. "Jaw-dropping, difficult to wrap your brain around, alternative reality" would come closer to an apt description. God proclaims that his answer to the problem of violence in Israel will be Babylon: the pagan, know-nothing about Yahweh, worshipping other gods, soul-crushingingly-powerful nation of Babylon. This is the evil empire of the Bible; a nation so infamously etched in the memory of God's people that the writer of Revelation would still use them as a code name centuries later for the pagan, know-nothing about Yahweh, soul crushingly-powerful empire of his own day (Rome). In spite of this, God intends to use Babylon to clean up Israel.
This is a hard pill for Habakkuk to swallow to say the least. Habakkuk questions it, wondering how a holy God can use such an unholy instrument to correct the people God called to be holy. It is in the midst of this exceedingly strange circumstance, this frighteningly new and uncertain action by God that we hear the words "The righteous will live by his faithfulness." The call of God through Habakkuk is for the righteous to live out of faithfulness (whether their own or God's is, perhaps purposely, ambiguous)** even in these violent and terribly uncertain times.
In the context of Romans 1:17, the quote from Habakkuk is often seen as a call to a righteousness by faith rather than by works. Correspondingly, the whole of Romans is thought to be Paul's detailed exposition of the righteousness that comes through faith in Jesus rather than good deeds. There may be a shade of truth to such a reading of Romans but I think that truth has more to do with Martin Luther's guilt-laden conscience and his reading of Paul than it has to do with Paul's own writing.*** Instead, if we allow the narrative of Habakkuk to set the tone for Romans as Paul himself seems to do, we will find that there are remarkable similarities between the two.
Similar to what we have seen in Habakkuk, much of Paul's writings are about the strange, completely unexpected, frighteningly new thing that God has done in Jesus Christ. No one, no one, expected a crucified messiah. "Crucified" and "messiah" are themselves mutually exclusive terms. If you were one, you couldn't be the other. As if that weren't odd enough, Paul's experience was that Gentiles, not Jews, were the ones responding most readily to God's, that is, Yahweh's, the Jewish God's crucified messiah. These were strange, new actions on God's part, indeed. So strange that Paul referred to them as a new era, a totally new epoch in the history of the world, the beginning of a new creation.
With this in mind, we can see why Paul would feel the need to say that he was "not ashamed of the gospel" (a religion with a crucified leader would have been a very shameful thing) but we can also see why he would call it the "power of God" (powerful enough to cause non-Jews to proclaim Israel's failed messiah as "Lord"). We can see just how it is that "the righteousness of God is revealed in it" as it makes sinful people (Romans 1-3) into righteous, just, and faithful people (Romans 6 and 8); something God's own perfect law had been powerless to accomplish (Romans 7). Likewise, we can see that just as the prophet Habakkuk has some questions about God's righteousness, Paul wonders aloud how it is that God will remain faithful to the promises God made to the people of Israel (Romans 9-11) even as this new righteousness/faithfulness is revealed in Christ (Romans 3-5). But in the midst of all this newness and uncertainty, the call upon those who proclaim Jesus as Lord is to live out of the faithfulness of Christ into a faithful imitation of Christ (1:17; chapters 12-15).
After 2000 years of Christian history and tradition, we too easily forget what an odd thing it is that we, who are nearly all Gentile, worship a crucified Jew. By doing so, we also forget what a strange, new thing God did in Jesus. If we read it carefully, Romans will help to remind us just how unbelievably good this good news really is for us. It will remind us that God keeps his promises even when it looks like they are most certainly being abandoned, whether it be as Abraham raises the knife over Isaac or as Jesus lays in the tomb or as Paul's kin reject their own savior. It is especially in these most uncertain of times that God calls the righteous to find in God's own faithfulness the source of their endurance to live faithfully.
*This is my own translation. Readers familiar with most English translations may be surprised by my use of the word "faithfulness" rather than "faith." The Greek word Paul uses here can be translated either way and really means both. Separating faith as a kind of mere cognitive belief from faithful action would have likely been a foreign idea to Paul. The single word faith/fulness encompassed both and bound them together. Furthermore, the Hebrew word Habakkuk uses has a much stronger leaning toward the idea of faithfulness than mere belief.
**It is ambiguous for a couple reasons. First, the "his" in Hebrew probably refers to "the righteous one" but it is possible that it refers to God. Second, the Greek version of the Old Testament known as the the Septuagint, reads "my faithfulness" and portrays the verse as being spoken by God thus making it God's faithfulness. To make things even more interesting, Paul leaves out the pronoun entirely in his quotation of the verse so rather than "his faithfulness" or "my faithfulness" we have simply "The righteous will live out of faithfulness." This serves Paul's purposes well because he wishes to talk about both God's faithfulness in Christ and and faithful human response.
*** There are a plethora of books that make this argument. A few are:
Krister Stendahl's Paul Among Jews and Gentiles. http://www.amazon.com/Paul-Among-Gentiles-Krister-Stendahl/dp/0800612248/ref=sr_1_1?ie=UTF8&qid=1379470781&sr=8-1&keywords=paul+among+jews+and+gentiles
E.P. Sanders Paul: A Very Short Introduction. http://www.amazon.com/Paul-A-Very-Short-Introduction/dp/0192854518/ref=sr_1_2?ie=UTF8&qid=1379470965&sr=8-2&keywords=e.p+sanders