When presidents shake-up or change-up their staff these days, I’m always reminded of this story Abraham Lincoln once told.
After his election in November of 1860, Lincoln attempted to reach out to every faction of his party in an effort to create a cabinet that would unite the Republican Party. 
Lincoln’s eventual picks included ALL of his main rivals for the Republican nomination. He was not intimidated about surrounding himself with those whom he fought on the campaign trail, even if their resumes for the presidency were more impressive than his own.
By the time the Civil War entered its second year, it was no secret around Washington that some of Lincoln’s Cabinet still considered him inadequate for the job as president.
In 1862, with the forced resignation of his Secretary of War Simon Cameron because of allegations of corruption and poor management in the War Department, a group of supporters urged Lincoln to use it as an opportunity to reorganize the rest of his cabinet.
“Gentlemen, when I was a young man I used to know very well a Joe Wilson, who build himself a log cabin not far from where I lived.
Joe was very fond of eggs and chickens, and he took a very great deal of pain in fitting up a poultry-shed. Having at length got together a choice lot of young fowls [chickens] – of which he was very proud – he began to be much annoyed by certain little black animals with white strips which it is not necessary to name.
One night Joe was awakened by an unusual cackling and fluttering among his chickens. Getting up, he crept out to see what was going on. It was a bright moonlight night, and he soon caught sight of half a dozen of the little pests, which, with their mother, were running in and out of the shadow of the shed.
Very wrathy, Joe put a double charge into his old musket and thought he would ‘clean out’ the whole tribe at one shot. Somehow he only killed one, and the balance scampered off across the field.
In telling the story, Joe would always pause here and hold his nose.
‘Why didn’t you follow them up and kill the rest?’ inquired his neighbors.
‘Blast it,’ said Joe, ‘it was eleven weeks before I got over killen’ one. If you want any more skirmishing in that line, you can do it yourselves!'” 
Lincoln never reshuffled his cabinet. Five [including Cameron] of the original eight resigned for various reasons over the course of four years, but he asked for no resignations.
Lincoln understood skunks.
Do presidents today?
Food for thought.
[Like this one? Please click here for more Stories That Abe Told.]
 Goodwin, Doris Kearns (2005). Team of Rivals: The Political Genius of Abraham Lincoln. New York, NY: Simon & Schuster. ISBN 0-684-82490-6
 Gross, A., & Lincoln, A. (1912). Lincoln’s Own Stories. Collected and edited by A. Gross. With portrait. Harper & Bros: New York & London. pp.98-99.