What are some fairly short novels that you would recomend that relate to American history during the early 1900's?
There are many novels set in the early 1900s that might be of interest to you.
For example, the Willa Cather trilogy about immigrant life on the Great Plains in the early 1900s is a good choice for someone who is interested in rural America and the immigrants who settled there.
For a look at what was going on in the urban areas of America, an obvious choice would be The Jungle by Upton Sinclair. You might also look at Sister Carrie, by Theodore Dreiser, which was written in 1900.
For something a little less highbrow, you could try Ragtime, by E.L. Doctorow. Depending on how far you would allow "the early 1900s" to go, The Great Gatsby is of course a classic.
If you're willing to go a little before 1900, Devil in the White City is set in the 1890s. It's not exactly a novel, but it is written more like a novel than like nonfiction.