When I was a 2L, I saw Justice Scalia give a speech to the Baltimore Federalist Society Chapter. Someone asked him whether the Solicitor General should be considered the "Tenth Justice." Scalia scoffed at the question, and said that there were only nine Justices. Still, as I recall, Scalia acknowledged that the federal government was a special litigant before the Supreme Court. Indeed, the Solicitor General is the representative of a coordinate branch of government.
Historically at least, the Solicitor General, received some special treatment. The SG had the highest number of cert petitions granted. Moreover, the Solicitor General is uniquely skilled at opposing certiorari by finding, and in some cases inventing, vehicle problems. The SG routinely obtains leave to participate in oral argument. These requests are rarely granted for any other party. The Court often invites the SG to offer views on a particular case. Critically, however, when the SG files an emergency motion with the Court, the Justices have treated the case with urgency.
Yesterday, the Supreme Court split 5-4 in Department of Education v. California. The majority seems to have treated the Solicitor General's application with the sort of comity that was due to a coordinate branch of government. Indeed, it remains unclear to me why this deference was not granted to the even-more-pressing USAID case.