Ralph Baze and Thomas Clyde Bowling Jr., two Kentucky inmates, are asking that very question. Three years ago, the inmates "brought suit in federal court…questioning the state's chemical mixture and the procedures used to administer it," says an article on www.cnn.com, because some prisoners felt extreme pain during their executions.
According to the same article, "The Supreme Court has not ruled directly on the 'cruel and unusual' aspect of lethal injection, but did conclude last year that prisoners can make last-ditch legal challenges to the method of execution, using claims that they would suffer a painful death."