Fourteen years and numerous judicial reviews have passed since José Medellin was sentenced to die after confessing to the brutal gang rape and murder of two teenage girls in Houston. That's long enough, state officials say. It's time to carry out the sentence. But defense attorneys, and an unusual coalition of federal officials, including no less than the attorney general and secretary of state, say if his Aug. 5 execution is not stayed, so Mr. Medellin's case can be reviewed one more time at the behest of the International Court of Justice, Texas will be rushing to judgment and endangering...