Statutory Debt LimitLet's quickly dispel a myth. The US debt position is rather comfortable. Moody's and S&P took away their AAA rating for political reasons, not economic ones. Following the last statutory debt limit crisis, they both expressed concerns (which indeed turned out to be true) that another such crisis may occur.
What is the statutory debt limit? In the US, the maximum dollar amount of obligations the Government holds (i.e. debt) is set in law. That is done to provide Congress with oversight over Federal borrowings, as part of the American Separation of Powers doctrine. When the total amount of public debt reaches (or nears) the statutory limit, the Treasury takes 'extraordinary measures' to ensure it is able to continue paying off its obligations. As the article states, that usually is enough for a few months - probably more than is publicly stated, but they stray on the safe side. I believe this was first done in the 90's, during Clinton's Presidency. Following that, the US would have to default on its debt as it would not be able to continue paying off its obligations, as it needs to borrow more money beyond the debt limit to pay off interest on its previous borrowings. That won't ever happen unless Republicans go absolutely batshit insane.
(By the way, the system of 'borrow money to pay the interest on previous borrowings' is completely normal, and does not suggest an uncomfortable debt position. All countries in the world do that to maximise their ability to spend money and minimise interest paid.)
There is a Constitutional argument that the
14th Amendment voids the debt limit. It states that "
The validity of the public debt of the United States, authorized by law, including debts incurred for payment of pensions and bounties for services in suppressing insurrection or rebellion,
shall not be questioned." As those borrowings are required by law (appropriation legislation), the argument goes that the 14th Amendment requires them to be paid-off, regardless of the debt limit. President Clinton
supports this theory, but it appears that the Obama Administration does not.
So that's that about the debt ceiling.
Expiring ProgramsThere are all sorts of taxes which will go up if a deal is not reached. The expiration of the Federal income tax cut enacted in 2001 and 2003 ('Bush tax cuts') is what has been receiving the most attention in the media. It appears likely that on this issue they will settle at extending them for all taxpayers except for households earning more than $400000 a year.
The payroll tax holiday which has been signed into law by Obama and subsequently extended until the end of 2012 has been receiving very little interest in comparison, albeit being quite significant. The
payroll tax is levied on employees and is how they buy into social security and medicare. For a few years its rate was cut from 6.2% to 4.2%, and it will go back up at the end of this year. Regardless of other political happenings, extending the tax holiday is out of the question (unfortunately), which is why it is not usually considered part of the fiscal cliff.
Other taxes which are scheduled to go up are
Capital Gains Tax and the Estate (inheritance) Tax. These are major points of contention between Democrats and Republicans, as they mostly affect higher-income taxpayers.
Federal Unemployment Benefits are also scheduled to end, however it seems increasingly likely that they will be extended.
Another barely-understood aspect of the fiscal cliff is the
Alternative Minimum Tax (AMT) affecting more and more middle-class taxpayers. The AMT is calculated separately from the regular income tax, and the taxpayer must pay the higher of the two. When it was designed in 1969, it was only supposed to affect the richest 155 taxpayers - but the American tax code is shitty like that.
The 'doc fix' is yet another issue. In 1997, a policy was enacted to reduce payments to Medicare providers by tying them to a lower inflation-adjustment calculation than the one which was used. Each year afterwards (with a couple of exceptions), Congress has delayed the implementation of this policy, so that doctor payments will not go down. If another 'doc fix' is not enacted, payments to Medicare providers will go down 27% starting 2013.
Furthermore, all kinds of tax credits and spending contained in the Recovery Act ('the stimulus bill') are set to expire over the next few months. This is entirely expected, and won't have such a large impact as they have been slowly wound down.
Overall, the decrease in income should all tax cuts expire is seen here:

The reason why higher-income tax-cuts will be especially hit also has to do with new taxes contained in PPACA (
the healthcare law).
SequestrationAusterity, basically.
If you guys remember, in July 2011 we had a similar panic about the debt limit being reached. As part of the
deal between Obama and House Republicans, a bipartisan Congressional
committee was formed to find at least $1.2 trillion in savings over 10 years. Obviously, being a bipartisan entity in the US, it failed miserably. Instead, spending cuts specified in the deal will now occur automatically. They are referred to as 'sequestration' or 'the sequester'.
The sequestration cuts are split roughly 50-50 between defence and non-defence spending. Government agencies will be hit, with many lay-offs possible. Pentagon spending will be cut by 9.2% while non-defence agencies will see a cut of 8.4%. However, entitlement programs will not be hit under sequestration.
http://www.politico.com/story/2012/12/sequestration-where-will-the-cuts-hit-85385.htmltl;dr: look here!