Here’s how it works at the USSC. All but a couple of justices are part of a pool of justices and all the petitions are distributed to the clerks for the Justices. For the most part, only one clerk for one justice reads - maybe - each petition; and then writes about a one-page summary with a recommendation to either grant or deny review. There is a great deal of pressure to simply recommend denial of review.
It is also true that the Court has greatly reduced the number of cases it accepts for a decision on the merits. Where they used to take over 200 cases a year, they are hardly ever deciding even 100 per year.
Unless you have a high-powered lawyer you are pretty much screwed no matter how badly your rights were abused in the lower courts.
Because of this, state supreme courts pretty much know they can screw you over and get away with it; especially in cases involving government corruption at the state level.
Unfortunately, I know this from personal experience.
What Orly Taitz submitted in Noonan v Bowen was not a Petition for a Writ of Certiorari but an application for a stay. Any one Justice can approve an Application for a Stay. In Noonan v Bowen both Justice Kennedy, the circuit Justice for California and Chief Justice Roberts declined to issue the requested stay. Roberts referred the application to the full Court but there were no takers.
Dr.Taitz was asking the Court to stay events that had already taken place before the Supreme Court received the application; a tough task.