The issue in the case is (taken from SCOTUSblog -- I tried to read the petition, but the process of opening the pdf froze the browser, which means that this is the second time I am writing this particular post):
Whether application of New York's state constitutional “meaningful representation” standard to evaluate Sixth Amendment claims of ineffective assistance of counsel results in decisions that are "contrary to, or involve an unreasonable application of, clearly established federal law" as required by the federal habeas statute.
If you want to read more about the Second Circuit decision, you can read my prior posts: here, here, here, and some media attention here. Just to note, in the Second Circuit it was called Rosario v. Ercole.
Outside of the interesting issue, there are some notable aspects to the Supreme Court case so far (which is probably why it's the petition of the day). First, three amicus briefs in support of the petition were filed (from The Innocence Project, The National Association of Criminal Defense Lawyers, and the National Association of Legal Investigators).*
*These last two are listed with an "et al," which probably means that other groups joined these briefs. But once again, I was unable to open the pdf's. At least this time I acted preemptively and saved my work before the browser froze.
The other very notable aspect of the cert. petition is that the Court ordered the State to respond. Quick Supreme Court Lesson: after a party files a cert. petition, the other side has the opportunity to respond. But in many situations, the opposing party can waive its opportunity to file a response. The petition then gets put on for a conference. But , sometimes, before getting reviewed in conference, the Court can ask that the opposing party respond. It only takes a request from one judge in order for the Court to order a response, but you never learn which judge ordered the response. If a response is requested, the case gets taken off the conference list and put on a new conference list once the petition is fully briefed (the original party who filed the petition will typically file a reply after the opposing party files its response).
The big deal about the Court asking for a response is that it dramatically increases the chances that the Court will grant cert. Maybe dramatic is too strong. But it goes from basically zero (no response requested) to a little above zero (if response requested). In other words, in my experience, the Court won't grant cert. unless it has actually received a response from the opposing party (either because the opposing party originally filed one in response to the petition or the Court ordered the party to file one). There are probably examples out there that proves that statement wrong, but I am guessing that it's generally true.
In Rosario, the response hasn't been filed yet (it's due in April). I guess it's something to keep an eye out for.