What is the origin and meaning of "attitude" when used without the
modifiers "good" or "bad," and as shown in the following two examples:

"She has an attitude." Does it mean she has a bad attitude?

"She has attitude." Does this variant mean she has a combative
attitude, but one that's not entirely negative in effect?

Hello nautico,
"An attitude" is a usage that has been around for some time. To say
someone "has an attitude" is often an expression of disapproval,
usually said about someone who is being high-handed, tempermental,
uncooperative, superior, and/or just plain difficult.(See also:
"Striking an attitude", which according to Webster's New World
Dictionary, Third College Edition, means "to assume a posture or pose,
often an affected or theatrical one.")

But, depending on the context nowadays, possession of an attitude can
be good. Take this website for example, created by a sports fan who
wanted a place where people could freely express their opinions:
www.sportsrant.com.  "Sports talk with an attitude"
Attitude here seems to mean no holding back, no matter how negative or
controversial the opinion may be.

In-your face self-assertion and confidence, without inhibition, is
what having attitude is all about, in the contemporary sense. And
since a picture is worth a thousand words, I refer you to this image
of "attitude" (or "tude" in slang shorthand):

http://www.photos-of-the-year.com/challenge/showphoto.php?photo=4454&password=&sort=1&page=1&thecat=500
The little girl in this photo is expressing her personhood in no
uncertain terms...no camera-shyness here, no inhibition. The photo's
title: "She's got attitude."

I hope this helps.
scribe_ga

Great answer and one that reflects my own reactions to this usage.