Griffin, whose term expires in November, will argue the case shortly before the labor board itself changes from a Democratic to a Republican majority. Two NLRB nominees are pending in the U.S. Senate—William Emanuel of Littler Mendelson and Marvin Kaplan, a federal agency lawyer. Bloomberg BNA reported Monday that Peter Robb of Downs Rachlin Martin in Vermont is a leading contender to replace Griffin for general counsel, a Senate-confirmed post.

"The board and the private parties, in advocating for their respective interests, differ in the emphasis placed on various arguments supporting their common position that the agreements are unlawful under well-established federal labor law and the FAA does not mandate their enforcement," Griffin wrote in urging divided time for himself and Ortiz.

On the other side, the government's top lawyer, Wall, has requested 10 minutes of argument time as a friend-of-the-court supporting the companies in the case.

Hogan Lovells partner Neal Katyal represents Murphy Oil and Epic Systems. Williams & Connolly's Kannon Shanmugam is counsel to Ernst & Young. Wall said in his request that they have agreed to cede 10 minutes of their 30 minutes to the government.

Neither Katyal nor Shanmugam immediately responded to requests for comment on whether they had agreed yet on who would argue for their clients or whether to seek a division of their 20 minutes.

If the two veteran high court litigators fail to agree, they can always resort to a coin toss—not unheard of within the court's marble walls.

Last year, two other high court veterans—Sidley Austin's Carter Phillips and Seth Waxman of Wilmer Cutler Pickering Hale and Dorr—initially sought to divide their 30 minutes so each could argue in key patent cases. But the justices, as they have with prior requests by private parties, denied their motion.

And so a coin was tossed. Phillips won.