These days, having the guts to do something just means someone is brave enough to take on what seems to be an overwhelming undertaking. Any herculean task could require guts: quitting a job, suing city hall, or voting third party could all require a gut check by today's standards. In days past, however, a gut check was only required by the soldiers who were about to fight in combat.
Armies in the days of yore – before the 20th Century – faced very different problems than the ones deployed American troops face today. Where we have been known to wince every time we see a runner missing his reflective belt or wonder why I always get the goddamned vegetarian MRE, the Army of the pre-World War I days was more worried about things like clean drinking water, cholera, and dysentery.
In days gone by, if someone asked a soldier if they had the guts to fight the coming day or the next day, it wasn't just an affirmation of macho willpower, it was a real question of a soldier's ability to maintain his position and discipline in the ranks instead of running off to the latrine every ten minutes to evacuate his bowels.
The asker's "gut check" was real – and literal – checking to see if his comrade in arms was suffering from diarrhea or a similar illness of the bowels that would keep him from performing at the front lines. Maintaining the integrity of certain infantry formations used to be integral to the survival of the whole unit.
At the time of the U.S. Civil War, microbes were only just being accepted as cause for disease. In that war, 620,000 men were killed, but disease actually killed two-thirds of those men. A single illness such as measles could wipe out entire units. Battlefield sanitation was the order of the day, but if Civil War troops chose to ignore an order, that would be the one. Latrines were dug near camps, wells, and rivers as horse and mule entrails and manure permeated their camps.
As a result, dysentery was the single greatest killer of Civil War soldiers. Having the guts to fight only meant you were one of very few troops not suffering from the trots.