Correction: "the JIG is up." Below is a link to a site that explains that "jig" is the correct spelling. Sorry, but it truly drives me nuts to see people spelling Jig, the J-sound word, as Gig, hard G-sound.

If you don't want to click on the link, the most likely etymology is a reference to the Irish dance, the jig, being over ("coming to an abrupt halt" )

https://crossidiomas.com/the-jig-is-up/