As Mr. Whelan said, “We all know how problematic e-mails can be.”

If there is a fight brewing over Ms. Kagan at all, it seems to be over the records. Mr. Sessions has been pressing hard for them, and warned in the interview that Republicans might use the filibuster to block Ms. Kagan’s confirmation if all the documents are not released in enough time for senators to review them before the start of the hearings, now scheduled to begin June 28.

Image Elena Kagan, on Capitol Hill in May, has met with about 50 senators. Hearings on her nomination are to begin this month. Credit... Stephen Crowley/The New York Times

“We would not like to filibuster,” he said, “but I would say a failure to produce documents and actions in that vein could lead to more tension than some people might expect.”

Senator Patrick J. Leahy, the Vermont Democrat and Judiciary chairman, said Republicans were trying to use a double standard. “We’re going to have far more documents than we had for Roberts and Alito, and a lot sooner,” he said in a telephone interview from his home in Vermont, referring to the two justices nominated by former President George W. Bush, John G. Roberts Jr. and Samuel A. Alito Jr.

Conservatives and liberals alike are eager for the documents; both sides would like to gin up a little bit of controversy, if only to energize their bases in this midterm election year. Nan Aron, president of the Alliance for Justice, a liberal advocacy group, said the records had the potential to transform Ms. Kagan “from a candidate who’s a blank slate to one with a very complex, intricate portrait.”

In the weeks since her nomination, Ms. Kagan has been making the usual courtesy calls to senators. So far, she has visited more than 50 of them, a parade of mostly ho-hum sessions that Dahlia Lithwick, who writes about legal issues for the online magazine Slate, has aptly dubbed “the Elena Kagan Bore ’Em to Death Tour.”

So far, only one Republican, Senator James M. Inhofe of Oklahoma, has said outright that he will not vote for her.

Others, including Mr. Sessions, say they have serious questions about Ms. Kagan, citing her lack of experience  she has never been a judge  and her decision to briefly bar military recruiters from facilities at Harvard Law School while she was dean. Yet the complaints seem to have gained little traction.