Cf. SUPREME COURT PRACTICE, 8th Edition, the ultimate SCOTUS resource.
As reported on earlier here, the Leo C. Donofrio suit may have legal legs to stand on. The Supreme Court has taken an extraordinary expedited action in fast tracking the New Jersey Citizen's suit challenging the presidential election.
It is unclear whether the stay application has now been accepted in lieu of a more formal full petition for certiorari (and/or mandamus or prohibition). It would be unusual if this was the case since it is rare but it was used in Bush v. Gore, 531 U.S. 98 at 98 (2000):
"The court ordered all manual recounts to begin at once. Governor Bush and Richard Cheney, Republican Candidates for the Presidency and Vice Presidency, filed an emergency application for a stay of this mandate. On December 9, we granted the application, treated the application as a petition for a writ of certiorari, and granted certiorari." (Emphasis added.)
The case has certainly been "DISTRIBUTED for Conference", a process usually reserved for full petitions of certiorari. Stays are usually dealt with in a different manner.
The stay application was originally denied by Justice Souter but under Rule 22.4, Donofrio renewed it to Justice Thomas who did not deny it.
A renewed application is rare.
Justice Thomas has referred the case to the full court.
That much is clear from looking at the docket.
In any case, although it is unclear whether the full court has set this for Conference, or Justice Thomas has done it on his own, the action signifies an affirmative action inside the US Supreme Court testifying to the serious issues raised by this law suit.