A majority of six Justices voted to deny the stay in an unsigned order, with Justice Harry A. Blackmun and John Paul Stevens joining Justice Ginsburg in opposition. While Justice Ginsburg's vote did not affect the outcome, it provided the first indication that she may take a different approach to questions on the death penalty that did her predecessor, Justice Byron R. White.

Justice White rarely if ever voted to grant any of the numerous applications for stays of execution that reach the Court, and he was in the 5-to-4 majority in two cases last term in which the Court rejected constitutional challenges to the Texas death penalty statute. Lawyers for the inmate in today's case, Johnny James, raised a similar challenge to the Texas law and asked the Court to overrule the two recent decisions.

Because neither the majority nor the dissenters wrote opinions explaining their votes today, there was no way to know whether the Court considered the underlying issues or whether, by contrast, the application was rejected for essentially procedural reasons. 'A Moral Victory'

Brent Newton, a lawyer with the Texas Resource Center in Houston who represented Mr. James, said he interpreted Justice Ginsburg's vote as an indication that she might be willing to reconsider the recent precedents that upheld the Texas law. "Getting her vote is a moral victory for us," Mr. Newton said.

Mr. James was sentenced to death for kidnapping and killing a woman in 1985. His conviction and sentence have been upheld by the Texas state courts and, most recently, by the United States Court of Appeals for the Fifth Circuit, in New Orleans, which rejected his petition for a writ of habeas corpus that challenged the constitutionality of his death sentence, as well as for a stay of execution.

An alcoholic who was drunk when he committed the crime, Mr. James argued that the Texas death penalty law unconstitutionally limited the jury's ability to evaluate his alcoholism as a factor that lessened his moral culpability and therefore argued against imposing a death sentence.

Four years ago, ruling in the case Penry v. Lynaugh, the Supreme Court found that the Texas law was constitutionally flawed because it did not permit a jury to give adequate weight to a capital defendant's mental retardation. The Texas law, which has since been amended, required the jury to decide whether a convicted murderer presented a future danger to society. In the Penry case, the Court found that this requirement made it more likely that a jury would weigh retardation as an argument for the death penalty rather than as a factor against it.