I'm assuming since you mentioned clerkships that you are going for DOJ or something along those lines. Your grades do have to be higher to get those kinds of jobs, but if you have something else going for you like Moot Court or law review it will even itself out.
I disagree that DOJ is an option for anyone with sub-median grades from Cardozo, even with law review or generic moot court experience. Although, stellar moot court performance and increasing grades to top 25% could make a difference.
From my understanding government positions are, generally speaking, not as concerned about your grades and school reputation when compared with private firms. The exception would be the high legal positions with the government like the US Attorney's office.
All employers care about grades and school reputation. The difference is that government pays much less, so typically students with top grades and top reputation do not work at government jobs. The self-selection involved with students' decisions does not necessarily mean government employers care less about these factors. But government employers typically have to be less picky because most of the high-grade and high-school reputation students prefer to find work elsewhere. But all else being equal, government litigation departments generally look to those who already have some litigation skills (as evidence by courses, externships, clinical, moot court, etc.).