I figured it out. Bear with me here...
If a site has an RSS (live headline feed), it will have a small icon that's orange with white stripes in the bottom right corner of the broser window. Click on it and "subscribe to whatever". Then you can save it as a bookmark.
Then open a second browser window. Go to -> bookmarks -> manage bookmarks. Drag that bookmark over to the other browser window and dump it in the top portion of your browser. Close all browser windows.
That's it. When you reopen firefox, it will automagically refresh the feed line and populate it with the headlines for that site/section. The Associated Press site has a list of its feeds here:
http://hosted.ap.org/dynamic/fronts/RSS?SITE=AP&SECTION=HOME The "default" rss feed will have a mix of the headlines. The list of shortcuts on that page can be used to make your own rss feed by clicking on the "properties" and changing it to the particular feed you want. Instead of the default "TOPHEADS.rss", I used the "BUSINESSHEADS.rss". It's actually pretty easy once you do it.
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Forgot to ask that you post the sites you find using rss feeds here.
Slashdot:
http://slashdot.org/Associated Press:
http://hosted.ap.org/dynamic/fronts/RSS?SITE=AP&SECTION=HOMEYahoo (you'll have to cheat a bit with the "properties" thing to make it work):
http://news.yahoo.com/rssexample of business headlines feed location = http//rss.news.yahoo.com/rss/business
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I can't get the yahoo thing to work (it's supposed to be only for "my yahoo" pages), but it does have some links to C|net, Washington Post, etc. that do work.