Here's a rough idea of what I had in mind:
1901 -- McKinley survives the attempt on his life
1902 --
Philippine Organic Act passes (as OTL)
1901-04 -- McKinley's second term goes less well than his first -- the 1902 Coal Mine strike grows violent (no WH intervention), and there is little action against trusts; the war
1904 -- William Jennings Bryan defeats Nelson Aldrich for the Presidency
1905-08 -- Bryan Presidency very chaotic and grows quickly unpopular
1905 (circa) -- Phillipine hostilities are declared at an end (bringing about sooner Phillipino self government); (also, the Russo-Japanese War lasts three months longer than OTL, due to a lack of US mediation, leading to a more radical 1905 Revolution in Russia)
1906 -- Sinclair's
The Jungle doesn't lead to any organized political response, but does lead to a slew of muckraker reports on the food industry; this poor response from Washington, combined with an economic crisis following the San Francisco earthquake, lead to major Socialist gains in Congress and at the state levels
1907 -- the economic crisis deepens as the Bryan administration falters
1908 -- Charles W Fairbanks defeats Bryan's bid for re-election; the Socialist candidate, Eugene Debs, receives nearly as many votes as the incumbent President
1909-12 -- the Fairbanks Presidency is confounded by crises
1909 -- Government is does little ambitiously, looking instead to overlook a slow recovery
1910 -- Socialists continue to do well, as Jackson Stitt Wilson wins the California Governorship, while John W. Slayton wins in Pennsylvania
1911 -- the recovering economy is imperiled with war breaking out in Europe
Election of 1912 -- President Fairbanks, under intense stress and growing unrest, declares he will not seek a second term
--the Republicans, not expecting to need another nominee, deadlock and end up nominating Speaker Joseph Cannon
--Theodore Roosevelt leads a group of splitters, running as an "interventionist independent"
--the Democrats, meanwhile, split between the Bourbons, who nominate Champ Clark, and the Populists, who bolt, and re-fuse with the People's Party; before the latter gather to nominate a candidate they are approached by the SPA...
--the Socialists nominate Pennsylvania Governor and noted party speaker John Slayton, who begins an outreach to Progressive Republicans and Populist Democrats
--faced with the prospect of nominating William Bryan as their candidate, delegates for the People's Party move toward a deal with the Socialists for a joint run, leading to Slayton's Populist nomination
--in a four way race, Roosevelt comes in fourth (with over 5% of the vote but no states), Joseph Cannon comes in third, Champ Clark comes in second, and Slayton -- with less just over 40% of the popular vote and 267 ECVs -- wins the Presidency