There were calls for Sherman to run for President after the Civil War; he resisted but WI he'd run in 1868 instead of Grant?
I believe this occured in 1880 when Sherman lost to James Garfield. I cannot recall if he was a candidate in 1876.if memory serves me correctly, John Sherman attempted in 1876 to position himself as the Republican candidate but failed to gather enough supporters at the convention.
The convention where John Sherman had the best chance was probably 1888--he actually led on the first six ballots. https://en.wikipedia.org/wiki/1888_Republican_National_Convention
He would most likely have won in November, too. He might have lost the 15 electoral votes of IN, where Harrison had a home-state advantage--but that would still leave him with a 218-183 lead in the Electoral College. https://en.wikipedia.org/wiki/1888_United_States_presidential_election
There is no reason to think Sherman would have lost Harrison's second-narrowest state in 1888--New York. Cleveland had only carried New York very narrowly even in 1884, and he had a whole lot of disadvantages in 1888 he didn't have in 1884: Conkling, who had helped to "knife" Blaine in 1884, was dead; Sherman (like Harrison) was less vulnerable than Blaine had been on the "character" issue; there was no "rum, Romanism, and rebellion" gaffe in 1888; and Cleveland's stance in favor of lower tariffs may have hurt him with industrial workers and specifically his stance in favor of placing wool on the free list,hurt him with a lot of Upstate sheep farmers.