Zinn deals with this topic in the most detail in Chapter 13 of A People's History. Essentially, he argues that socialism reached a sort of high-water mark during the Progressive Era, owing largely to the many problems that had resulted from the rise of industrial capitalism, viewed by Zinn as utterly exploitative. Where Progressives attempted to enact reforms that would address many of these social ills, socialists (like Zinn himself) saw the problem as being rooted in capitalism itself. Zinn peppers his account with discussions of Socialist heroes like Eugene V. Debs, "Mother" Jones, and Helen Keller, and outlines the rise of radical unions such as the Industrial Workers of the World, who broke with powerful craft unions like the American Federation of Labor and took a leading role in many labor disputes during the period. Zinn shows that radicals, especially socialists, found allies among black workers, women, and especially the millions of immigrant workers. They all agree, Zinn claims, on one thing:
...that they could not count on the national government. True, this was the "Progressive Period," the start of the Age of Reform; but it was a reluctant reform, aimed at quieting the popular risings, not making fundamental changes.
This claim, while betraying a rather flat analysis of the very nuanced Progressive movement, is fundamental to Zinn's interpretation of the period. While angry radicals challenged the very heart of industrial capitalism, alarmed businessmen turned to Progressive establishment politicians for protection. The price of this strategy was that they had to be willing to accept reforms. Progressive politicians, whether "honest reformers" like Bob La Follette or "disguised conservatives" like Theodore Roosevelt were mainly interested in fending off the threat represented by socialism and other forms of radicalism. According to Zinn, they wanted reform as a means of bringing about "class peace," and while he concedes that "ordinary people benefited to some extent" from Progressive reforms, he frames them as essentially conservative. He concludes his chapter with the violent miners' strike at Ludlow, Colorado in 1914, suggesting that this event demonstrates the extent to which the Progressives failed to defuse class conflict in the nation. Having failed through reform, he suggests, politicians would soon turn to war.
Source: Howard Zinn, A People's History of the United States, pp. 314-349.