Moran, Daniel Keys. The Armageddon Blues
Divergence: 1962 CE
Summary: In 1968, a woman from 2731 meets an immortal born in 1712, and they set out to prevent the nuclear war of 2007.
Published: Bantam/Spectra 1988 (0553271156). Revision of "All the Time in the World", in Isaac Asimov's Science Fiction Magazine, May 1982.