Some of the earliest references to the word "whoop," and what I would argue are the relevant references to "big whoop," were unfortunately racist references to Native American war cries. References to "war whoops" and "savage whoops" are not hard to find in 19th-century newspapers in the United States and earlier. In nationalist white sentiment, the idea of a "big whoop" therefore came to mean "a big cry," or a big deal made of something, usually which was being mocked.
OED confirms this angle on the term "whoop":
a. An act of whooping; a cry of ‘whoop!’, or a shout or call resembling this; spec. as used in hunting, esp. at the death of the game, or by N. American Indians, etc. as a signal or war-cry (see also war-whoop n.); occasionally the hoot of an owl.
Early newspaper references to a "big whoop" express this mocking intent. First a headline picture, then a snippet from an article in the same print.
A Big Battle Between the Crows and Sioux.
A Band of 1,000 Indians - From Whoop-Up Land.
A party of six men arrived at this place yesterday from Fort Benton, making the trip in canoes in ten days. The simple announcement of such an exploit conveys very little idea to the general reader of just what the journey really is. The distance is some 1,200 miles, through an unbroken wild and hostile country, and the way is beset with dangers from the outset to the close. Just previous to the party leaving Benton, news was brought to that fort that the British troops had entered the "Whoop-up" country, and that trouble with the American trappers there was imminent.
"Terre Haute, Indiana, is to have a new paper, to be edited by three women." That will be the paper for news. Three women in one sanctum! Our "devil" says he'd like to be there, just to raise one big whoop.
By the 1880's, the term "Big whoop" seems to have become established as a sarcastic term meaning "a big deal made of something," usually in a hopeless fashion.
He arranged who should be nominated in advance, gave his ticket to Col. Johnson to be nominated by the Assistant Republican Association, had the judicial conventions to endorse those nominations, and then had the Republican State Convention to endorse them all in a big whoop. Now that kind of proceeding is evidence of a machine.
The term meaning "a big deal" in a sarcastic or mocking way caught on so rapidly and with such strength that most users of the phrase today have little awareness of its origin. Today, "big whoop," as the other answers and the original post indicate, simply means "big deal," sarcastically.