The main things here I think would be:
* Some US drop shippers may need a sales tax ID and other documentation if they are going to be shipping to US customers. I think you'll find that some will be willing to work with you, but others may just say no because you are based in the UK.
* You need to list the location of the items in your eBay listing. Seeing you are going to use US drop shippers and list on eBay US, this will be to your advantage.
* Doing some research into the US market will be important, as there will no doubt be some differences between the US and the UK.
* Testing the items and delivery will be very important. Because you are quite removed from your supplier, it's going to be really important you know their business inside out, test the quality of their products for yourself, and find out what shipping options they use and what these are like. You won't have much control over what goes on, yet any customer complaints/questions will come to you, so you will need to be well prepared.
Hope that helps! If you need help with doing some more research into this, please don't hesitate to ask.