Do you start work on the same month as the start date on your opt card? If so, I don't see a problem with starting work merely 2 days before your card gets there. You will be paid for that month anyways, and more often than not, your paycheck won't specify what dates in the month you worked; it will just say you worked the month of June, for example. 

Even if it isn't the same month, I don't think it is a big deal. Is it legal? Technically, no. Will there be consequences if you start a couple days early? I highly doubt it. Fret not, start your work. I wish you good luck in your new job.