Friom my experience, it will be there first think the next morning, shipped to your doorstep. If they dont know its an alive creature, they might leave it on your doorstep and if they do they will take it back to the nearest shipping office if im not mistaken. Your best info would be from the person you bought if from, or go to the currior's website. Anyways, expect it first thing next morning and be ready for it so it doesnt sit around unattended.
First, if it's US Mail priority, it will take 2-3 days to get there. Second, do you know what days they ship on? Alot of online dealers only ship on certain days of the week. Just to let you know as well, these dealers aren't sitting there waiting to pack up every order as soon as they come in. If you ordered it last night, the earliest it will probably even be packed is sometime today. Most good dealers wont ship at the end of the week on the off chance that the T will get stuck somewhere over the weekend. I suggest that you call the dealer you ordered from and find out when they're going to ship the spider and when you can expect it. Personally, I wouldn't expect it till next week sometime.
If it cost $17.50, it should be express mail, which is normally supposed to be delivered the next day, unless we're talking remote areas or the package was shipped late in the day. If the shipper checked the "signature required" box, the postman should bring it to the door and knock. Of course, that doesn't mean they actually will...When you talk to the shipper, ask for a tracking number. This will help the PO find the package if it gets lost.