I don't have a featherweight but when I got a needle stuck in a thread nest, I carefully released the screw that holds the needle in place. Make sure you turn off the machine before proceeding. With the needle released you can turn the hand wheel to bring up the needle receptacle and give yourself a little more room to work. Next remove the foot on the machine if possible. Open the bobbin area and see where the needle is. Can you remove the bobbin case or is the needle inserted into it? If so, see if you an wiggle out the needle from the top with a pair of needle nose pliers.
Hopefully someone that owns a featherweight can give you more advice.