My college roommate wrote a history thesis that went on to be published in the Berkeley Undergraduate Journal. His essay concerned views of Providence from both sides of the Civil War. Providence is the belief that God will provide in one's favor despite adverse circumstances. He argued that Christian leaders from both North and the South firmly believed that God would vindicate their respective causes. He cites Abraham Lincoln's second inaugural address in 1865:
Both read the same Bible and pray to the same God, and each invokes His aid against the other. It may seem strange that any men should dare to ask a just God's assistance in wringing their bread from the sweat of other men's faces; but let us judge not, that we be not judged. The prayers of both could not be answered. That of neither has been answered fully. The Almighty has His own purposes.
Lincoln acknowledged that both North and South believed that God was on their side. And it was only in the aftermath of the South's defeat that anyone could say that the North was right, slavery was wrong, and justice was exercised. But it wasn't clear then. And it certainly wasn't clear to Southern Christians. Lincoln's speech demonstrates that although the North won, it doesn't mean the North was "right". After all, we prevailed over Native Americans but that didn't make it "right".
My point is not everything is black and white. It is possible to be a committed follower of Jesus and have widely divergent political views from other Christians.
Most political views of a given issue hinge upon one's view of the role of government. Generally speaking, a liberal view sees government playing an active and moral role in the public sphere. A conservative view tends towards the other extreme. A libertarian view eschews government intervention in many arenas and relies upon market forces and constitutional rights.
Below are three possible affirmative action stances with their corresponding biblical justification. It is in no way intended to be a comprehensive; it's just a quick gloss I came up with based on my understanding of Christian ethics.
1) In support of affirmative action - fight injustice
Zechariah 7:9-10 "This is what the LORD Almighty says: 'Administer true justice; show mercy and compassion to one another. 10 Do not oppress the widow or the fatherless, the alien or the poor. In your hearts do not think evil of each other.'
God commands his followers to fight for justice on behalf of the orphan, the poor, and the oppressed. Christians are commanded to do the same. There is a systemic injustice in the form of racial discrimination that severely inhibits the progress of under-represented minorities like Latinos, blacks, and refugee Asian groups (Laotians, Cambodians). Due to the hardships these ethnic groups face, it is vital to help even the playing field and consider race in college admissions. Since a college education is one of the best ways to achieve socioeconomic progress, affirmative action gives students from under-privileged backgrounds a chance at the American dream.s
2) Against affirmative action - support outreach programs
Colossians 3:11 Here there is no Greek or Jew, circumcised or uncircumcised, barbarian, Scythian, slave or free, but Christ is all, and is in all.
This passage teaches that followers of Jesus, no matter their race, nationality, ethnicity or socioeconomic status, are united in love through Jesus Christ. Because race is secondary, we should not neither discriminate against nor in favor of. To do so would be fighting injustice with injustice. However since structures of injustice still exist and need to be addressed, it is far more effective and desirable to promote state-sponsored outreach programs at the preschool and K-12 level in economically disadvantaged areas. This is the way to live out the command of Zechariah 7:9-10 without in the spirit of Colossians 3:11.
(I recognize this passage can just as easily be used to justify affirmative action as much as against it. The same applies to slavery as well.)
3) Against affirmative action - live kingdom values in your own community
Acts 17:7 and Jason has welcomed [Paul and Silas] into his house. They are all defying Caesar's decrees, saying that there is another king one called Jesus."
This view is more difficult to justify explicitly with a single verse but a theme runs through scripture involving the king and his kingdom. The Jews expected Jesus to be a political messiah - one who would deliver them from Roman oppression. Jesus was nothing like that. Rather, as Christians, we expect political justice upon his second advent. There's a theme (especially in the apocalyptic literature of Daniel and Revelation) that emphasizes both submission to and distrust of, governmental authority. God is the highest authority. The government, therefore, has no business playing God and should stay in its lane. It means as Christians we are skeptical of the government's role and activate ourselves as the church to fight injustice. This means living out redemption in the communities where we live.
Personal conclusion: There are strengths and weaknesses of each view and I've vacillated between each one. Right now, I'm not wedded enough to any one stance to fully commit. If you pinned me down, I would probably pick 1 or 2.