PLEASE PLEASE DO NOT DO THIS!!!!
There was an article in "Birds and Blooms" about the fabric and thread getting wet causing the baby birds to die of the cold and damp.
I don't know who thought of this but they are terribly wrong if they think it is a good idea. If you want to give the birds nesting material then use pet or human hair. I'm sure if you went to a local beauty salon or pet groomer they would let you have hair to put out for bird nests.
One fall after the leaves had fallen I saw a nest made up of gray hair, that was the neatest looking nest I had everseen.