It does not mean what you think it means and I feel bad when I hear them smart folks on the TV use it.
"Begs the question" is not synonymous with "insists upon the obvious question;" If something "raises a question" it does not mean it "begs the question."
"Begs the question" is the name of a logical fallacy in which the proposition's truth is assumed true and stated or secreted away within the premises. Here's a properish usage:
"The guy's a god-damn Cat Owner."
"How do you know?"
"Because he owns a cat."
"But that's begging the question!" *~jazz hands~*
"I'll beg your question, you god-damn catlover-loving freak!"
It's not the easiest thing to identify sometimes, although wikipedia does a better job than they used to, less jargon-y than most of their math and logic articles.
Unless you're one of those folks who thinks usage gradually becomes correctness when the improper usage becomes the dominant form which makes sense I suppose and then you can go ahead and keep on using it incorrectly irregardlessly.
This Diary is dedicated to my phantasy lover, Ms. Rachel Maddow.