After nearly three hours of arguments, Judge Mary Jacobson said "important issues of constitutional significance" would take time to review. She asked the legislative committee to submit additional legal arguments by Monday.
Kelly and Stepien will have until March 24 to respond.
Kelly, who appeared in court Tuesday, seemed on the verge of tears outside the courthouse, where she was confronted after the arguments by a throng of television cameras and news reporters.
Her lawyer, Michael Critchley, said she was "a 42-year-old single mom of four children, trying to make do in a difficult time."
Stepien did not appear in court. His lawyer, Kevin Marino, said he was "an innocent man . . . and someone who has very much the same right to express his Fifth Amendment privilege as someone who is in fact guilty of a crime."
Christie announced during a Jan. 9 news conference that he had fired Kelly and cut ties with Stepien after the release of e-mails that suggested his aides were involved in orchestrating lane closures at the George Washington Bridge that snarled traffic in Fort Lee over four days in September.
The e-mails - provided to lawmakers by former Port Authority of New York and New Jersey official David Wildstein - included an August message evidently sent by Kelly to Wildstein that read, "Time for some traffic problems in Fort Lee."
They also included correspondence between Wildstein and Stepien, who called the Fort Lee mayor "an idiot" in an e-mail following the lane closures.
Some have speculated the closures were in retribution against the borough's mayor, a Democrat, who did not endorse Christie's reelection.
Federal prosecutors also have been investigating the lane closures, while the legislative committee has issued nearly 40 subpoenas, including those to Kelly and Stepien. The subpoenas seek text messages, e-mails, and other communications about the lane closures, dating to September 2012.
Marino argued Tuesday that the committee did not have enough evidence to subpoena the records from Stepien.
To justify the subpoena, the committee needs proof that more records involving Stepien exist and that they are in his possession, Marino said.
He said the panel had provided five e-mails connected to Stepien. "Five e-mails do not permit the fair inference there are other documents," Marino said.
Critchley said the committee could not prove the "traffic problems" e-mail was sent by Kelly, undercutting the basis for the subpoena.
"I am not conceding that," he said. "Nor do I have to concede any element of proof" that could incriminate Kelly.
Ordering Kelly to respond to the subpoena would be the same as forcing her to testify, which would violate the Fifth Amendment, Critchley said.
And if Kelly turned over documents, it could be argued that she had waived her Fifth Amendment privilege - putting her at risk of being forced to discuss the material she had provided, Critchley said.
Reid Schar, outside counsel to the legislative committee, said there was a difference between providing documents and testimony.
The committee is not asking Stepien or Kelly to explain what the documents mean, Schar said. Any subpoena seeking records has "a minimal testimonial" aspect, he said.
Schar said the committee was not engaged in a "fishing expedition." The panel, he said, has received "a number of additional e-mails" connected to Kelly or Stepien.
"I don't need to guess, Judge," said Schar, adding, "There are additional documents." He did not elaborate on the contents of the e-mails.
In her questioning, Jacobson drew a distinction between Kelly and Stepien, noting that Kelly was a public employee, subject to public records rules.
There also was an inconclusive discussion of the committee's powers and whether granting immunity would be a way to get the documents. Schar said the panel should not have to do so to obtain them.
"To get around these issues, they could just give us immunity," Critchley said.
However, he said, the committee does not want to grant immunity, which he said would apply to the federal investigation.
Assemblyman John S. Wisniewski (D., Middlesex), cochair of the committee, said after the hearing that immunity offers would need to be addressed "with other agencies."
"I'm not sure that a legislative investigatory committee that's looking at changing the laws so future abuses of power can't happen is where their concern lies," he said of Marino and Critchley.