My baby shower was scheduled for my 37th week of pregnancy. If you have any say at all, DO NOT let this happen. Aside from the obvious issue of possibly missing your own shower due to early delivery, here are some other problems with such a late date:
1. You are pooped. The shower was on Saturday and I basically slept all weekend and am still recovering on Tuesday. It was a great time but seriously too much for me just now, not to mention the 6 hours of car time to get there and back.
2. You end up waiting a really long time to do your own shopping. I'm now wiped out with only 3 weeks left to go and rushing around trying to buy, wash and organize the remaining registry items. It would have been so nice to have this all done by now. This also meant I had to put the nesting on hold, which was SOOOOOOOOOOO hard to do. Every time I bought anything I got a lecture about how I should wait until after the shower and I just wanted to be done and ready.
3. This is the time you want to be stocking up on rest more than anything else. I think that shower took the last of my energy and I'll end up spending the next few weeks sleeping as much as possible.
Anyway, it was a lovely shower, and thrown by my SO's family so I didn't want to be rude and turn it down. However, if I were to do it again, I would have made it more clear that I wasn't willing to travel so late in my pregnancy. If you have any input on your shower date at all, try to have it before week 35 and try to be closer to home, and if possible not in your own home (we had one of those too and we're still cleaning up).