What is the biggest tire I can put on a stock 2001 Electra glide classic?

 

You should find there is plenty of room for an MU/85, which is one size wider than stock. An MT is 130mm wide, an MU is 140mm.

You may just about get in a 150/80, but not everyone has been successful. That is the widest size it is wise to fit on a stock 3" rim. The limitation is clearance with the belt. You can best measure this by removing the belt guard. You can fit a narrow spacer behind the rear pulley, but there is limited clearance between the pulley and swingarm!

Also be aware that the actual fitted width of tyres is not constant and can be different between brands. For example Avon 150/80 V speed rated tyre is wider than their H rated.