The phrase "huge wrench" means a large, heavy tool used for twisting and turning objects, like nuts or bolts, that is much bigger than usual. Full definition
A two meal service was easy logistically to run lean and mean staffing and prep wise, but a third meal threw a huge wrench in the operations. (whiteonricecouple.com)
As the demonstrators were rallying on Varick Street, Trump was busy at the White House throwing a huge wrench into the discussions about immigration and a fix for the dangers facing the nearly million residents in the US under the Deferred Action for Childhood Arrivals, or DACA, program by referring to Haiti, El Salvador, and African nations as «shithole countries.» (gaycitynews.nyc)
Moving definitely throws a huge wrench into workout plans. (fairyburger.com)