Mainly because our Labor Movement was pretty well suppressed.

In the late 19th Century and during the Progressive Era strikes were extremely common. This paper by Janet Currie states that between 1881 and 1894 there were 12,964 labor strikes. One quote in the introduction to the paper strikes me as relevant to your topic:

The period that we examine -- the 1880s and 1890s -- was among the most contentious in American labor history. It was also a crucial turning point: By the beginning of the twentieth century, labor had largely abandoned politics and adopted a philosophy of "business unionism" -- a focus on "workplace concerns achieved through collective bargaining and industrial action on the shop floor" rather than the approach adopted by European unions which aggressively "advocated workers' interests in the political arena, and advanced an extensive program of state-sponsored social reform"

Basically part of the reason was that labor unions in America began to abandon politics is that employers and laborers here stopped focusing on politics, unlike Europe. I think that needs some elaboration, though. For that I'd like to look at Philippe C. Schmitter's "Still the Century of Corporatism?". Basically, European systems began to evolve into what is called a "Corporatist" mode of organization. This has nothing to do with Libertarians' attack on today's capitalism as corporatism, by the way. It's basically a system of interest representation that seeks to balance the demands of many different interest groups in a nation, with labor and employers being two of the primary groups involved. To do this, there are hierarchically arranged unions covering an entire group (one large Shoemaker's Union, for instance).

For labor to be represented, they need to have a specific political party, which of course leaves all the European nations with Labor Parties and large umbrella unions. However, Schmitter called the United States "pluralistic," meaning that our system of interest representation is not state licensed nor are unions stretched over entire groups. Thus we have many different unions within the same field, leading to them being isolated from one another more so than in Europe. This means that no contiguous labor party can come together and enter US politics. And after the 1920s the attitude of the US turned against Unions (except among the poor, but they were of course disregarded, but I'll cover that in a second), which meant that even if the US started to move towards a more corporatist system the political climate has not been there.

However, much of the lack of a Labor Party (and Labor Movement in general) is because our government actively suppressed it. Strikes were often violently broken up, and hundreds of strikers killed. Labor was also pretty much gutted under the Coolidge Administration during the 1920s, which left it even more defunct than in the past, killing its potential to expand and push the US towards a corporatist system.

I hope that helped! I'd recommend reading all of Schmitter's essay, even though it's super long it's fascinating.