The airlines want to start the trial in November.
The Justice Department said in a court filing Tuesday that given the stakes in the merger -- it would create the world's biggest airline -- it needs more time to prepare.
The government accuses the airlines of rushing the case.
The judge plans to hold a conference on the schedule Friday, but it's not certain that she will set a trial date then.
The government says the merger will reduce competition and drive up travel prices. The airlines say it would provide more competition by creating a third big airline to rival United and Delta.