In a letter sent Tuesday to the outside counsel representing the panel, Stepien's lawyer, Kevin Marino, said Stepien had not changed his position.
"I can think of no lawful way the committee can obtain documents responsive to its subpoena from Mr. Stepien," Marino said in the letter to Reid Schar, also describing the committee's investigation as "politically charged."
If the committee does not withdraw the subpoena, Marino suggested, he and Schar should discuss "a schedule for seeking a judicial determination" into the matter.
Assemblyman John S. Wisniewski (D., Middlesex), cochair of the legislative committee, said Tuesday that the panel was not backing down.
"We're going to continue our efforts to enforce our subpoena served on Mr. Stepien and to obtain the documents the committee seeks," Wisniewski said. He declined to specify how lawmakers and Schar might respond.
"I don't want to discuss our strategy publicly," Wisniewski said. Of the likelihood the matter would go to court, he said: "Clearly that is one option."
Wisniewski said the committee had not received any new communication from Kelly's lawyer but pointed to news reports Tuesday that she also was refusing to comply. The lawyer, Michael Critchley, did not return messages Tuesday.
Christie fired Kelly and cut ties with Stepien last month after the disclosure of e-mails indicating an apparent plot to jam traffic in Fort Lee by shutting access lanes to the bridge in September.
In August, Kelly sent an e-mail to David Wildstein, then an official at the Port Authority of New York and New Jersey, that read: "Time for some traffic problems in Fort Lee."
The e-mails - which were turned over by Wildstein under subpoena - showed Stepien mocking the Fort Lee mayor. Some have alleged that the closures were intended as retribution on the mayor, a Democrat who did not endorse the Republican governor's reelection.
Christie has denied any involvement in the lane closures and has said he did not know of them until they were over.
Federal prosecutors also are investigating the lane closures.
The legislative committee's probe widened last week with the issuance of a new round of subpoenas, some of which focus on the testimony of former Port Authority official Bill Baroni. Baroni, a Christie appointee, told lawmakers that the lane closures were part of a traffic study.
Baroni resigned in December along with Wildstein, who told Kelly, "Got it," in response to the "traffic problems" e-mail.
Why Kelly sent the "traffic problems" e-mail is the biggest question facing the committee, Wisniewski said.
With nearly 40 subpoenas issued since January, "most of what we're doing now is waiting for documents to come in," he said.
Wisniewski said Schar had received unredacted documents from Wildstein, whose original 900-page submission included a number of blacked-out sections.
Some of the new information should be included in the committee's investigation, Wisniewski said. He said Schar was working with Wildstein's lawyer.
But "there's nothing in there that is extraordinary," he said.