I think that Zinn would answer that the sacrifice of human progress is the voice of dissent. The narrative that Zinn constructs regarding the progress in the United States is one in which every step towards advancement results in a step of destruction for someone or something else. The "progress" that enabled Columbus to find land resulted in the destruction and enslavement of indigenous peoples. The "progress" of American innovations such as the cotton gin and the factory system resulted in the enslavement of people of color and the suffering of millions of workers in the North. As the nation moved from farms to factories, progress was realized in those who owned the means of production at the cost of those who suffered in squalor and in the worst of living conditions.
Zinn paints the picture that the sacrifice of human progress is a voice of dissent that advocates a sharing in the ownership of the means of production. Such a sacrifice further advances the wealth and power of the few at the cost of the many. For Zinn, the sacrifice of human progress in American History is voice and the ability to articulate what can and should be in the face of what is. It is this narrative of American History that Zinn unabashedly states must change so that "progress" can become a more inclusive term that seeks to advance the interests of all "the people" and not just a few of them.