The high court will hear a challenge from two inmates on death row in Kentucky - Ralph Baze and Thomas Clyde Bowling Jr. - who sued Kentucky in 2004, claiming lethal injection amounts to cruel and unusual punishment.
Baze has been scheduled for execution Tuesday night, but the Kentucky Supreme Court halted the proceedings earlier this month.
In another important case, the court agreed to decide whetherunfairly deter the poor and minorities from voting, stepping into a contentious partisan issue in advance of the 2008 elections.
The U.S. Supreme Court has previously made it easier for death row inmates to contest the lethal injections used across the country for executions.
But until Tuesday, the justices had never agreed to consider the fundamental question of whether the mix of drugs used in Kentucky and elsewhere violates the Eighth Amendment's ban on cruel and unusual punishment.
All 37 states that perform lethal injections - including Texas, the nation's most active death penalty state - use the same three-drug cocktail, but at least 10 states suspended its use after opponents alleged it was ineffective and cruel, according to the Death Penalty Information Center.
The three consist of an anesthetic, a muscle paralyzer, and a substance to stop the heart. Death penalty foes have argued that if the condemned prisoner is not given enough anesthetic, he can suffer excruciating pain without being able to cry out.
U.S. District Judge Aleta Trauger ruled last week that Tennessee's method of lethal injection is unconstitutional and ordered the state not to execute a death row inmate using that method. The state is still deciding whether to appeal the judge's ruling, but agreed to stop a pending execution.
A ruling from California in the case of convicted killer Michael Morales resulted in the statewide suspension of executions.
States began using lethal injection in 1978 as an alternative to the historic methods of execution: electrocution, gassing, hanging and shooting. Since the death penalty resumed in 1977, 790 of 958 executions have been by injection.
"Right now there seems to be a working majority on the Court - Justice Kennedy and the four more liberal Justices - who would be willing to strike down lethal injection as a form of capital punishment until and unless the procedures used to employ it are improved," said CBS News legal analyst Andrew Cohen. "So don't be surprised if that's the ultimate result here."
Baze and Bowling sued in 2004 and a trial was held the following spring. A state judge upheld the use of lethal injection and the Kentucky Supreme Court affirmed that decision. The appeal taken up Tuesday by the U.S. Supreme Court stems from that decision.
"This is probably one of the most important cases in decades as it relates to the death penalty," said David Barron, the public defender who represents Baze and Bowling.
The office of the Kentucky attorney general had no comment Tuesday on the case.
Baze, 52, has been on death row for 14 years. He was sentenced for the 1992 shooting deaths of Powell County Sheriff Steve Bennett and Deputy Arthur Briscoe.
Bennett and Briscoe were serving warrants on Baze when he shot them. Baze has said the shootings were the result of a family dispute that got out of hand and resulted in the sheriff being called.
Bowling was sentenced to death for killing Edward and Tina Earley and shooting their 2-year-old son outside the couple's Lexington, Ky., dry-cleaning business in 1990. Bowling was scheduled to die in November 2004, but a judge stopped it after Bowling and Baze sued over the constitutionality of lethal injection.
Among other new cases the Supreme Court accepted Tuesday: