The execution was rescheduled for tomorrow at 2:01 a.m., "barring any legal impediments," said Brian Garnett, a spokesman for the Correction Department.
Yesterday's ruling to lift the stay was opposed by the high court's more liberal members -- Justices John Paul Stevens, David H. Souter, Ruth Bader Ginsburg, and Stephen Breyer.
Gerard Smyth, chief public defender for the state public defenders office, which had argued that Ross's mental capacity needed further evaluation, said the decision ends their attempts to block the execution.
A hearing on the restraining order was scheduled for 10:30 a.m. today before the US Court of Appeals for the Second Circuit in New York.
Under a warrant issued in October, the state has until Monday morning to execute Ross. If the execution does not happen by then, the state would have to go back to court to seek a new execution date, a process that could delay the execution for months.
Ross is on death row for strangling four young women and girls in eastern Connecticut in the early 1980s. He has also admitted killing four other young women in Connecticut and New York. Ross last year decided to fire his public defenders and forgo any remaining appeals.