Craig on Tuesday said he won't resign until "legal determinations" are made. A political source involved in discussions about the case said Craig has made it clear he wants to find a way to stay in office.
A court ruling on Craig's appeal could take longer than the four days before September 30.
In his petition to vacate the plea, Craig's attorney maintained the senator's "panic" over the possibility that the allegations would be made public drove him to accept a guilty plea without seeking legal advice and that he had been assured by the arresting officer that the matter would remain private.
The petition also claims that because Craig submitted his guilty plea by mail, he did not have the benefit of a judge explaining the exact consequences of the plea before accepting it.