That's a question explored by Linda Greenhouse in the New York Times today. She observes:
The Supreme Court has granted two stays of execution and refused to vacate a third in the three weeks since it agreed to hear a challenge to Kentucky’s use of lethal injection.
. . . .
The top criminal court in Texas, a state that accounts for 405 of the 1,099 executions carried out in this country since 1976, has indicated that it will permit no more executions until the Supreme Court rules, sometime next spring. The Nevada Supreme Court this week postponed all executions in that state. The governor of Alabama gave one inmate a 45-day reprieve. The country’s most recent execution took place in Texas on the night of Sept. 25, hours after the Supreme Court announced its review of the Kentucky case.