Lawyers for Bridget Kelly and Bill Stepien, two key players in the ongoing Bridgegate scandal, were in court Tuesday to make the case as to why their clients should not be compelled to turn over subpoenaed documents to the legislative committee probing the issue. Kelly's attorney says granting his client immunity would speed up the process.

The New Jersey side of the George Washington Bridge (Andrew Burton/Getty Images)

"What they could do," said attorney Michael Critchley, "to get around these issues is just give us immunity. They don't want to give us immunity. They can; they don't want to give us immunity. If they give us immunity, it applies to both federal and state."

That's the problem, according to Critchley. He said the committee doesn't want to interfere with the U.S. Attorney's probe into Bridgegate.

"You could have a compelling authority which could be the legislative committee or the state, they grant immunity and that'd also apply at the federal level," Critchley said. "They don't want to give us immunity. They can. They don't want to because I would assume they're working in a coordinated procedural path with the federal government."

The counsel for the legislative committee, Reid Schar, isn't sure the panel has immunity powers that are as sweeping as Critchley seems to think.

The lawyers for Kelly and Stepien argued that their clients should not be required to turn over subpoenaed documents to the legislative panel. The attorneys claim doing so would violate their clients' Fifth Amendment rights against self-incrimination. Schar disagrees. He said the committee has plenty of documents that prove Stepien and Kelly have information germane to the case. The judge did not issue a ruling.

It is widely believed that Kelly wrote the now-infamous email stating: "Time for some traffic problems in Fort Lee." Gov. Chris Christie had her fired the day after the email went public. Stepien was named by the governor to be chairman of the Republican State Committee and be a consultant for the Republican Governors Association. Both job prospects disappeared per Christie's wishes after Stepien became embroiled in the Bridgegate scandal.