Same situation for me, I've heard a few other people report it took up to two weeks for their codes to arrive. My advice would be to hang in there and if it hasn’t arrive after two weeks you could try contacting PlayStation Networks costumer support.
I received an invitation to Playstation Now on 3/27 and filled it out and sent it back. It said to "Keep an Eye on your Email in the next few days for your code." Well it's now 4/7 and I've yet to still receive the follow up email with my access code. Anyone else get this also?