Lincoln proved himself that day, as he did so many other times. Though he was sick on the day he delivered the Gettysburg address, he did not allow it to provent him from carrying out his duties.
The president found it in himself to show compassion for not only the fallen men, on both sides, of the Civil War and their families, he also found compassion for a young soldier who was accused of desertion.
When that soldier was sentenced to death, his father went to see Lincoln, begging for him to intervene. Lincoln did so, staying the young man's execution. It was not a particularly popular decision, but popularity was not Lincoln's goal. Perhaps that is one of the reasons why he is widely considered to be America's greatest president.