The phrase “come hell or high water” means: Let the consequences be whatever they may, however ill.
We’d say that this is considerably older than the date 1915, shown for it in A Dictionary of Americanisms.
In fact, we heard it commonly employed in Colorado and Wyoming some years earlier, and it is the sort of expression that one would expect to find studded through Bret Harte’s Western stories.
And, though the dictionaries describe “high water” as either being about the same thing as ordinary highest tide or ordinary highest flow of a stream, we’d translate the “high water” of this saying as referring specifically to the flash floods of water that roll down a canyon after a heavy storm above, sweeping everything before it.
Certainly that’s the kind of destructive force worthy of comparison with “hell.”
The expression “Come hell or high water” means “no matter what obstacles may be in the way.” For example “I’ll get to my grand-daughter’s wedding, come hell or high water.” This means no impediment will keep me from being there — not fire and brimstone nor the river rising. Compare to “I’ll be there – God willing and the river don’t rise.” Same kind of reference to the sort of natural obstacle that formerly would prevent someone from keeping a commitment. The expression is a reference to circumstances that might arise BEFORE an event, not the possible consequences THEREAFTER.