Annexing the Philippines had a very big effect on the US. It marked the introduction of European Darwinian racism into American culture. Support for black organizations that had existed in the North drained away and political representation of blacks disappeared. The number of blacks in both houses of congress had stabilized (at a low number, of course) after the end of reconstruction, but after 1899 the last few were given the boot in quick succession.
Also, IIRC, one of the top issues in the election of 1900 was imperialism. The democrats were still waving William Jennings Bryan around for all they were worth. Without that, the democrats might dump Bryan and go for a more typical politician (which might just work) or they might do just the opposite, and campaign on a more socialist platform (which almost certainly would not). There was a big coal strike right before the election, I seem to remember - that's probably their only hope. Later elections will, of course, be even more divergent.
I don't think this is as unlikely as it sounds at first glance. Just look at Cuba and Panama: Sure they were technically independent, but the US owned all the parts of their countries that it wanted and interfered in their affairs as often as it saw fit. It's a bit tougher, since they are farther away, but this way you can let Carnegie pick up the tab (Andrew Carnegie offered $20 million to purchase Filipino independence).