The independent prosecutor, Kenneth Starr, wants to question Mr Blumenthal not about the main allegation in the case - that Mr Clinton had an affair with the trainee, Monica Lewinsky, and told her to lie about it - but about a possible sub-plot. The specific allegations against Mr Blumenthal are that he orchestrated a media campaign against Mr Starr that was designed to move the spotlight away from Mr Clinton and on to the role, power and motives of the independent prosecutor.
Mr Starr is demanding that Mr Blumenthal, a former journalist, hand over records of conversations and meetings he had with reporters about the Lewinsky case. But in Washington, the very idea that Mr Blumenthal, a specialist in the art of media spin and massaging reporters, might be compelled to lay bare his strategy and methods, has been greeted with horror as it would threaten the cosy relationship between politics and media that makes the US capital tick.
The mini-contest between Mr Blumenthal and the prosecutor's office illustrates the extent to which the Monica Lewinsky case is developing into a personal confrontation between President Clinton and the independent prosecutor, Kenneth Starr, with aides and supporters ranged on either side. The Clinton camp, led by Hillary Clinton, regards Mr Starr as politically motivated - out to get the President by fair means or foul. They have accused his office of allowing, if not encouraging leaks of evidence damaging to Mr Clinton.
Mr Starr's supporters contend that he is only doing the job he was appointed to do: investigate allegations about the legality of Mr Clinton's conduct, first in the Whitewater land deal in Arkansas, and more recently in the Lewinsky case. Some of his recent moves, however - whether or not they were projected through Mr Blumenthal's lens - have attracted widespread opprobrium.
They include the aggressive questioning of Monica Lewinsky's mother, Marcia Lewis, about her daughter's relationship with the President. Ms Lewis broke down after two days on the stand and her lawyer is now petitioning for her to be relieved of any further obligation to testify on grounds of ill-health. The decision to have a mother testify about her daughter, while quite legal, has been condemned.
But harsh and distasteful methods have not been the exclusive preserve of the prosecutor's office. The Washington Post has given details of the line of inquiry being pursued by Mr Clinton's defence team in the sexual harassment case brought by Paula Jones. According to the Post, every aspect of Ms Jones's private life is being investigated. Former lovers, colleagues and employers have been turned up, all directed at presenting her as promiscuous and unreliable. That trial is set to come to court in Arkansas in May.
Back in Washington, the Clinton team may not be displeased with the multiplying subplots in the Lewinsky investigation, despite Mr Blumenthal's indignation. They serve to delay the star appearances in the case - expected testimony from Ms Lewinsky herself and perhaps also from Mr Clinton - and keep the public happily distracted.
The current mood - more redolent of a spectator sport than lofty legal argument - was summed up in reactions to a suggestion from Ms Lewinsky's PR-minded lawyer that his client was running out of money and needed a legal fund. Laughter, rather than tears, was the public response.