Maybe we should give AC a break. They had to combine old Canadian Plus accounts into Aeroplan before they could start issuing the Elite packages this year. And there are a lot more packages than before. It's not a simple matter to assemble them and get them mailed out.
Just because you don't have a package doesn't mean that you aren't recognized as an Elite. I've been getting Elite benefits since mid January when the computer systems were updated. You should have no problem getting into the lounge or using the priority check-in without the card. Just explain that you haven't received the package yet. The only problem I can see is upgrade certificates; perhaps, if you ask nicely, you will find a sympathetic gate agent.
My Elite package hadn't arrived yet when I was home last weekend. I won't be home again for another week. I'm not concerned.