Depends. I can deal with almost anything as long as it's the right size, gender, and has something resembling the correct weapon.
On the other hand, I usually choose not to - I have a lot of minis, and I enjoy buying new ones, so I'll often hunt around for one that looks very close. Sometimes, I go in the other direction too - if I find a really great mini in a story, or one I already have sparks my interest, I'll base the look of the character on the miniature. Rarely (if I'm really into the game, and I just can't find anything that makes me happy) I'll even convert a mini.