the globe theater in london during shakespearean times had a trap door on the floor of the stage when actors fell into it the fell onto a handbasket that was covered in pillows. the actors started calling it "going to hell in a handbasket.
In the US, the expression was used when Chinese railroad workers were lowered down mountainsides in baskets to place dynamite for tunnels. If the people pulling the man back up did not pull fast enough, the man was said to have gone "to hell in a handbasket".