Bruce, Smithsonian Folkways has a companion CD to the songbook KickyC quoted from, Sing For Freedom: The Story Of The Civil Rights Movement Through Its Songs, and it's available from Amazon (click for a sample) and the usual suppliers. The CD has recordings of "Eyes on the Prize" and also the original form of the song, "Keep Your Hand on the Plow." This is what the songbook says about the song:

This is a song that has been through every chapter of the civil rights movement. The words "keep your eyes on the prize" (replacing the more common "keep your hand on the plow") came from Alice Wine, one of the first proud products of voter education schools - on Johns Island, South Carolina in 1956.
The song had meaning for the sit-in students who were the first to be 'bound in jail' for long periods of time. It went with the Freedowm Riders to Jackson and into Parchman, and on to Albany and all of the many other areas of struggle.

The original song is also known as "Hold On." Here's a quote about that song from a book called Ev'ry time I Feel the Spirit, by Gwendolyn Sims Warren:

Struggling with the tribulations and hardships of slave existence, believers needed the encouragement of others not to give up but to hold on. As a later gospel song says, "Hold to God's unchanging hand" - trust in His deliverance, keep pressing on. this exhortation is based on Luke 9:62, which says, "anyone who puts a hand to the plow and then looks back is not fit for the Kingdom of God." Aother scripture, 1 Corinthians 9:10, says that those who plow should do so in hope.
"Hold On" imaginatively uses its imagery to hearten, exhort, and teach the message of the scriptures...The song's chorus talks to the whole slave community, from brothers and mothers to deacons and preachers. All must watch their step and hold on to the great gospel plow. The plow and track are interesting images because they related not only to the scriptural passages at the heart of "Hold On," but also to ordinary, everyday activities.

St. Paul talks about working toward a prize in Philippians 3:14 and 1 Corinthians 9:24, so the substitution of "prize" for "plow" seems to fit into the scriptural imagery of the song. The verses are flexible, many the same as those found in many other spirituals, plugged in wherever they fit.
It sure is a beautiful song, isn't it?
-Joe Offer-