The phrase “No picnic in May” was already a cliché in July 1861 when Melville wrote in the aftermath of Bull Run, also known as the Battle of Manassas. It was an unexpected defeat for the Union army that deflated expectations of an easy victory against the Confederacy and indicated a protracted war:

Who here forecasteth the event?
What heart but spurns at precedent
And warnings of the wise,
Contemned foreclosures of surprise?
The banners play, the bugles call,
The air is blue and prodigal.
No berrying party, pleasure-wooed,
No picnic party in the May,
Ever went less loth than they
Into that leafy neighborhood.

See: “The March into Virginia Ending in the First Manassas (July 1861)” was published in Battle Pieces and Aspects of the War 1866