I don't know where the idea of a .45 caliber actually came from, but there is an interesting (and AFAIK true) story that might shed some light.
When it was decided to replace the "trapdoor" with a repeating rifle, Frankford Arsenal set out to develop ammunition which would give the characteristics the army wanted. (Ammunition was always developed first, the weapons submitted for test having to use the specified ammunition.)
They settled on a .30 cartridge, with a bore diameter of .300" and groove diameter of .308". After the Model 1892 (Krag) was adopted, someone reportedly asked the Frankford Arsenal officer who had been in charge of cartridge development, how he came to choose .30 caliber, expecting a long talk about ballistics, lethality, accuracy, etc. Instead the officer replied, "Well, it seemed like a nice round number."
And that was how the rifle caliber to be used by the United States for the next roughly 70 years came to be set.