Heather Cook was due to go on trial last night accused of killing Thomas Palermo by hitting him with her car whilst drunk.
US media reports the postponement could be to provide more time for prosecutors and Ms Cook to agree a plea deal to prevent the need for a trial.
Ms Cook, 58, has already admitted hitting Mr Palermo but rejects all 13 charges against her, including manslaughter, driving under the influence of alcohol and leaving the scene of an accident.
She had been the second-highest ranking Episcopal leader in Maryland before the accident and the Church has since defrocked her.
Speaking outside court, David Irwin, Ms Cook's lawyer, said: "We would hope that we could resolve the case without trial for everyone's sake."
Alisa Rock, Mr Palermo's sister in law, said: "We will continue to be here for as long as it takes to get justice."
She declined to comment on the possibility of a plea deal.