"I'm talking about while in office," Judge Chin said about possible investigations while Mr. Trump is President. "Nothing could be done - that is your position?"
"That is correct," said Consovoy, who cast it as a temporary protection from investigation while Mr. Trump is President.
"This is not a permanent immunity,” Consovoy added.
This was not the first time that lawyers for the President had made this type of argument, as his attorneys - and top officials in his administration - have said that Congress has no power to investigate Mr. Trump, either.
"Article I grants Congress no express power to investigate," Treasury Secretary Steven Mnuchin said back in April, as the Trump Administration refused to give Congress the President's tax returns.
"Congress's investigative power is not unlimited," Mnuchin added.
The legal arguments on Wednesday in a tax return case came as another federal court ordered the State Department to give Congress a series of records related to Ukraine by late November.
That came as three committees in the House sent a letter to the State Department, reminding officials of a request for documents related to the Ukraine investigation.
"The Department has not produced any documents," the Democrats wrote, "in response to the subpoena issued...on September 27, 2019."
So far, the State Department and White House have not complied with a variety of subpoenas, along with multiple requests by Democrats in Congress for documents and other materials.
"President Trump has tried to obstruct the impeachment investigation by refusing to comply with doc requests, subpoenas & demanding administration officials not appear before Congress," tweeted Rep. Ed Perlmutter (D-CO).
The lack of cooperation by the White House and State Department has been undermined by a series of individual officials who have testified in recent weeks in closed door depositions.
Wednesday was another example, as a Pentagon official ignored orders not to testify, and cooperated with the investigation.
A series of State Department officials also ignored similar orders in order to give their testimony to lawmakers.