Asked what his committee's next move would be, Nadler was non-committal when questioned by reporters, as his panel will hold a first hearing on Monday about the Mueller Report, and the Russia investigation.
Democrats said that Hicks did turn over some documents from her time working on the Trump Campaign - but not from when she worked at the White House.
In a letter, White House Counsel Pat Cipollone said Congress was asking for documents which should remain confidential.
"Those documents include White House records that remain legally protected from disclosure under longstanding constitutional principles," Cipollone wrote.
House Democrats said they would not back down from their quest for more answers about the Russia investigation, as they said it is evident the White House is obstructing legitimate Congressional inquiries.
Already planning a vote next week to hold U.S. Attorney General William Barr in contempt of Congress, Democrats said others defying subpoenas might see a similar fate.
"There's definitely discussion about trying to group some of these contempt citations together as the Administration's contempt begins to manifest itself in committees and subcommittees throughout the Congress," said Rep. Jamie Raskin (D-MD).
Republicans said it was all political, and a waste of time.
"The 'Mueller Deniers' are at it again," said Rep. Kevin Brady (R-TX), as some Republicans said Democrats were clearly angling to start impeachment hearings.
But after a morning meeting of House Democrats, there was still no sense that Democrats were ready to launch such a historic effort.
"We're going to have to make the case," said Rep. Donna Shalala (D-FL), who urged hearings by the House Judiciary Committee about the Mueller Report.
"Laying out the case can't just be, because we don't like this man," Shalala said, referring to President Trump.