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(CNN) —  

Senate Democrats, eager to sink the nomination of Judge Brett Kavanaugh to the Supreme Court, are ratcheting up demands for a mountain of documents about his time working in George W. Bush’s White House, a sign that the high-stakes battle is quickly devolving into a process fight.

Republicans on the Senate Judiciary Committee began to discuss the matter Tuesday evening, but they had not yet made any determination on whether to ask the White House to turn over all the documents from Kavanaugh’s time as Bush’s staff secretary and as an associate counsel.

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Forcing the White House to turn over those documents could slow Kavanaugh’s nomination process, and potentially give Democrats new ammunition if any of the records reveal controversies from his past. But if Republicans don’t ask for those records, they could be accused of ignoring relevant details about someone whose rulings could reshape American life for a generation.

“The fact that they have chosen somebody who has a big paper trail is not our problem,” said Sen. Sheldon Whitehouse, a Rhode Island Democrat who sits on the Senate Judiciary Committee. “That’s their problem, and they need to be organized and get it to us.”

Ahead of an evening strategy meeting in Senate Majority Leader Mitch McConnell’s office, Senate Judiciary Chairman Chuck Grassley, an Iowa Republican, told CNN that no decisions have been made about which records to request from the White House, saying he needs to get a better “feel” for all the documents that are out there beyond the 300 opinions Kavanaugh authored as a federal judge on the US Court of Appeals for the District of Columbia Circuit. Grassley said it’s uncertain when confirmation hearings could occur because the relevant records need to be vetted first.

Other Republicans said there are limits.

“I think you can ask for too much,” said Sen. Orrin Hatch of Utah, a veteran GOP member of the Judiciary Committee who will meet with Kavanaugh on Wednesday, warning Democrats not to be “obnoxious” about their requests. “But there is a lot, a lot of documentation they are going to have to disclose.”

“I’m not sure it’s relevant to his job as a judge,” said Sen. John Thune of South Dakota, a member of Senate GOP leadership, when asked about the document requests related to Kavanaugh’s time in the Bush White House.

Kavanaugh’s paper trail is one reason that McConnell, a Kentucky Republican, advised President Donald Trump to consider other nominees who could be confirmed more quickly, ensuring the final votes occur ahead of the November midterm elections, when control of Congress will be at stake.

Democrats have already seized on the documents to make new demands, hoping to disclose controversies that could add new complications to Kavanaugh’s prospects in the narrowly divided Senate. Democrats say every document from his time in the Bush White House needs to be turned over to the committee, arguing that a similar standard was followed by Justice Elena Kagan in her 2010 confirmation proceedings.

“We need to look at his record, and his record isn’t only as a judge,” Sen. Dianne Feinstein of California, the top Democrat on the Judiciary Committee, told CNN.

“Are you kidding?” Sen. Richard Blumenthal of Connecticut, another Democrat on the committee, said when asked if Democrats were simply trying to slow down the fight. “These documents are all extremely relevant to his views on executive power and Bush administration policy, as well as current questions of presidential authority.”

Blumenthal added: “I mean, we’re not talking about high school term papers. His involvement in the Bush administration was one of the central parts of his career, and many other documents are relevant too.”

The White House is working on providing documents about Kavanaugh’s past to the Senate, but the scope of the records that will ultimately be turned over is unclear, sources said.

The White House plans to work with the Judiciary Committee to provide relevant documents about Kavanaugh’s past, according to a White House official.

Outside groups are also waging a battle for Kavanaugh’s documents. The group Fix the Court, which advocates for Supreme Court transparency and accountability, sued the National Archives and Records Administration and the Justice Department on Tuesday over outstanding requests under the Freedom of Information Act related to Kavanaugh’s time working under the former independent counsel Ken Starr, who was investigating the Clinton White House. The FOIA request, which demands notes and correspondence from 1994 to 1998 as Kavanaugh worked for Starr, could amount to some 20,000 pages, the group said.

And that is likely a fraction of the records, emails and documents Kavanaugh had a hand in while working in the Bush administration as an associate counsel from 2001 to 2003 and as staff secretary from 2003 to 2006 before being confirmed to the federal bench.

Some key Democratic senators said Tuesday that the more records turned over, the better.

“The more I have the better it’s going to be,” said Sen. Joe Manchin of West Virginia, a Democrat whose vote on Kavanaugh could be pivotal on the Senate floor.

Leaving McConnell’s office, Senate Majority Whip John Cornyn, a Texas Republican, said no decisions had been made about requesting documents from the White House.

“I think you will hear a lot about that,” Cornyn said. “It’s still being discussed. No decisions made.”

CNN’s Ariane de Vogue and Liz Turrell contributed to this report.