The Answerbag writes that arn makers found that dying wool before spinning it into yarn caused the fibers to better retain the color.  A popular comparison was to teaching children early to influence them in ways that would stay with them throughout their lives. The expression found its way into politics when Daniel Webster accused some Democrats of having attitudes as unyielding as the dye in wool. Of course, Democrats began to use the term to brand their opponents as unreasonably stubborn.