The expression comes from the JCB company, a UK-based manufacturer of heavy equipment founded by Joseph Cyril Bamford in 1945. It's like saying, "You'd need a bulldozer to dig yourself out of this."
From Ian Rankin's "Resurrection Men," an Inspector Rebus novel, Chapter 16:
"Fuck me?" Claverhouse was shaking his head. "You've got it all wrong, Rebus. It's you the boys in Barlinnie will be telling to bend over. Because if I can tie you to Cafferty and his operation, so help me I'll send you so far down they'll need a JCB to find you."