The late 1800's and early 1900's leading into to the Depression there was a materially pervasive threat of general insurrection and many disparate insurrections and armed struggles, especially involving the radical union comprised of Marxists and anarchists the Industrial Workers of the World, radical members of the reformist led Socialist Party of America, Western Federation of Minders, disenfranchised blacks and immigrants especially the Ukrainians, Finns and Russians among others. These organizations were hit hard by the first Red Scare and the workers' movement went underground but revolutionary politics retained a large following particularly among urban factory workers in the Northeast, Pacific Northwest loggers and miners and rural sharecroppers in the south.

The Comintern sent funds to help rebuild the American workers' movement which along with the inspiring example of the October Revolution caused most radicals to gravitate towards the Communist Party (or Workers' Party as its legal front was initially known) including many former IWW's like William Z Foster, James P. Cannon and Elizabeth Gurely Flynn. While many more moderate workers and Marxists remained in the Socialist Party which would be more electorally successful than the CPUSA but never have the same mass political influence. This would culminate in the mass movements around the Communist Party in the 1930's, including the Congress of Industrial Organizations, ACLU, unemployed councils movement, Sharecroppers' Unions, African Blood Brotherhood, ethnic and student federations and mutual benefit organizations like the International Workers' Order. This mass movement for a variety of reasons, including Comintern policy which favored collaboration with the US and a reduction in confrontation as well as a vacillating line on Germany depending on Russia's strategic needs, the split of the Trotskyists, the liquidationist policies of CPUSA leader Earl Browder who thought that class struggle in the US would diminish rather than grow, the second Red Scare and the accompanying repression like blacklists, banning communist immigration and union leadership as well as improved conditions for the largely white unionized industrial workforce with the New Deal Consensus, would ultimately fizzle out. The New Left of the 1960's would also pose a threat to the established order but that's an entire post unto itself.

While there was labor agitation before the early 1900's, it was largely disorganized and spread by the International Workingmen's Association as well as what would evolve into the Socialist Labor Party. The St Louis Commune of 1877 was the first important insurrection and despite being largely spontaneous was the most successful. The Colorado Labor Wars were fairly bloody and involved many extremely militant workers fighting against murder and violence by bosses in most cases in order to be treated like human beings. There were also various other labor insurrections and general strikes, like the Seattle General Strike and Pullman Strike, many of which were met with violence either from bosses or the state militia. As /u/ErdeTyrenne mentioned the Battle of Blair Mountain which took place in the context of the West Virginia Mine Wars, involving the bombing of US citizens by the government, and the Ludlow Massacre are particularly striking examples.

There were also concentration camps set up by the government in places like Coeur d'Alene Idaho and other places for striking workers, union organizers and members pressed into chain gangs and made to do forced labor fairly reminiscent of Gulags, laws passed like the Espionage Act that empowered vigilantes, and violent reprisals in Washington State by members of the American Legion against members of the IWW, an organization dedicated to establishing what they called the "Cooperative Industrial Commonwealth" where the workers would democratically control production and overthrowing capitalism, for their lack of patriotism. You also had armed action among loggers in the Pacific Northwest in the IWW to defend themselves against lynch mobs and similar actions in places like Montana among miners. Hundreds of thousands of unionists and political dissidents faced jailing, beatings, mob lynchings, forced labor, abduction, tarring and feathering, murder, legal and extra-legal harassment at various points during this period. Strikers faced violence from the state and business owners in part because of a real fear of anarchism and later Bolshevism. So overall it was a really turbulent time across the whole country where there was a lot of state repression and workers taking matters into their own hands, in many cases with an aim to establish some kind of socialism.

There was also the Green Corn Rebellion in Oklahoma in this period organized by sharecroppers and radical members of the Socialist Party (who received little support from the more moderate national organization)

You might also consider the Watts Rebellion which had some armed elements which was a movement of urban black people against white supremacy.

There were also wars of "pacification" against Native Americans after the Civil War and uprisings on reservations against genocide within territory claimed by the USA.

Of note is the Bonus Army led by Major General Butler which was comprised of WWI veterans who had mached on the capitol and were forcibly dispersed with tanks.

And there was also the Mormon insurrection in Utah and violent conflict in Missouri to establish their own country.

Great resources are Howard Zinn's A Peoples' History of the United States, the documentary Wobblies, The University of Washington Harry Bridges Center's website which has resources about the history of the Communist Party, IWW, and other labor related topics in Washington State, as well as Spartacus Educational's biographies of folks like William Haywood, Eugene V Debs, Frank Little and so on.

There were some insurgent activities by Confederate stalwarts but these weren't especially wide spread. There were also some insurgencies in local areas by free blacks, supported by the Freedman's Bureaus, against white populations (a notable example is outlined in US Marine General Lejeune's memoir). Though they didn't materialize necessarily, the estimate for the Louisiana example from the Lejeune source holds the armed black militia at over five thousand strong. Some white aristocrats and notables were assassinated, but the revolt was suppressed when the leaders were found and arrested.

It's unclear how close a communist insurrection in the US was to developing during the Great Depression, but the threat was serious enough for the creation of War Plan White, a serious Department of War draft to fight just such an insurrection in the event that it happened. We may never know how serious the threat was, but someone in the US government clearly felt it was dire enough to invest a lot of time in formulating and preparing for it.

Surprised no one mentioned the Wilmington Insurrection of 1898 in North Carolina. It's the only recognized coup d'etat in US history.

After conservatives lost the local election, Whites in Wilmington took up arms and ousted the newly elected government. The government they put into place quickly set up new Jim Crow laws and disenfranchised more African-American voters. The coup had a powerful impact on the South East in general.