This chart gives the dimensions of assorted threads..

Note that the 2-56 thread has a max diameter of .0854

If you want to cut your own threads your rods must be that size or slightly larger..

I've checked some of my rolled 2-56 rods and most are less than .08

The rodchuck folks recomend 3/32 welding rods for cutting 2-56..
http://www.rodchuck.com/

Don't use music wire.. it's to hard.. Trust me.. I ruined a 4-40 die trying.

Get Welding Rod.. You can get it in Stainless or mild steel.. the Rodchuck site has a good guide.