The Difference Engine
It posits a Victorian Britain in which great technological and social change has occurred after entrepreneurial inventor Charles Babbage succeeded in his ambition to build a mechanical computer (actually his analytical engine rather than the difference engine).
The novel is chiefly set in 1855. The historical background diverges from reality around 1824, when it is imagined that Charles Babbage succeeded with his Difference Engine and went on to develop the Analytical Engine. He became politically powerful and at the 1830 general election opposed the Tory Government of the Duke of Wellington. Wellington staged a coup d'etat in 1830 in an attempt to overturn his defeat and prevent the acceleration of technological change and social upheaval, but was assassinated in 1831. So the Industrial Radical Party, led by a Lord Byron who had not died in the Greek War of Independence, came to power. The Tory Party and hereditary peerage were eclipsed. British trade unions assisted the ascendancy of the Industrial Radical Party (much as they aided the Labour Party of Great Britain in the twentieth century in our own world). As a result, Luddite anti-technological working class revolutionaries were ruthlessly suppressed.
In the novel, the British Empire is more powerful than it was in our world, thanks to the development and use of extremely advanced steam driven technology in industry. In addition, similar military technology has enhanced the capabilities of the armed forces (airships, dreadnoughts, and artillery); and the Babbage computers themselves. Britain, rather than the United States opened Japan to Western trade, in part because the United States became fragmented, due to interference from a Britain which foresaw the implications of a unified United States on the world stage. Counterpart successor states to our world's United States include: a (truncated) United States; the Confederate States of America; the Republic of Texas; the Republic of California; a Communist Manhattan Island commune (with Karl Marx as a leading light); British North America (analogous to Canada, albeit slightly larger in this world); Russian America (Alaska); and terra nullius.
This has come about because the British practice a policy of "divide and conquer." They've "smuggled guns to the red-skins, to help them keep the Yankees at bay," says one character.
The scenario is consistent with what we've seen before in works of fiction. Namely, that the British didn't have the resources or the desire to conquer all of North America. Under their rule, it's likely the continent would've remained fragmented among several powers. That would've given some tribes the leverage to form alliances and stay independent.
British rule isn't a given, obviously. But the British narrowly lost the Revolutionary War and the War of 1812, and considered helping the Confederacy win the Civil War. Any change that stopped or slowed the US from sweeping across the continent would've aided the Indians.
In short, The Difference Engine gives us another scenario in which Native defeat wasn't inevitable. People who claim it was inevitable don't have very good imaginations.
For more on the subject, see 1824's Premise and Turning Points in Trail of Tears. For more on the subject in general, see "What If" Stories About Indians and The Best Indian Books.