1. debt ceiling: arbitrary limit the government can borrow to pay for things for which the congress has already approved. think of it as a permanent, never-ending mortgage that allows us to pay for stuff.
2. why it's a big deal: we're the United States, and our bonds (that's that perma-mortgage thing I mentioned above) always pay. If they don't, all hell breaks loose. Seriously. US Bonds are the ONE zero-risk investment in the world. If that fails, if that zero-risk becomes a non-zero risk, everyone on the planet is a potential victim.
3. democrats want: the ceiling to be raised, business to continue as usual, and potentially to actually borrow MORE money so they can get a few jobs programs running. They also want to allow the bush tax cuts to expire, which cut taxes for the wealthiest people in the history of the world, and if cut, would actually resolve our debt issues (after Iraq and Aghanistan come to an end).
4. democrats are willing to give on: sick people, poor people, extremely poor people, and extremely poor sick elderly people. (medicare, medicaid, and social security).
5. republicans want: the US to default, global calamity, world war III. you might think I'm joking, but they figured out the one thing from WWII that was lost on everyone else -- the rich get a whole lot wealthier during global catastrophes, even if they take a little blame in the short run.
6. republicans are willing to give on: nothing. they want to end the United States and reform it in their own image: a Militaristic Corporate Superpower, bought and sold by the global corporate oligarchy that runs it already.