In truth, Congress could do any of the above. The sequester itself is itself just a Congressional statute like any other and can be amended, overridden or replaced by another Congressional statute. Now, that doesn't mean the political will is there for some of the options you have laid out, but there is no requirement tied to the legislation passed during the debt ceiling negotiations last year that created the groundwork for the "fiscal cliff" that would actually prevent these scenarios from coming to pass.
So, the only thing Congress needs to agree to in order to address the fiscal cliff is some legislation that can get through both the House and Senate and be signed by the President (which is anything but an easy proposition as we have already seen).
The real question then is what options are politically palatable enough that they are being discussed.
There are two main components to the cliff. The first are a series of tax reductions that are set to expire at the end of the year including payroll, income, unemployment benefits, the Alternative Minimum Tax, and new taxes related to the Affordable Care Act (among others).
The second component are a series of automatic spending cuts, referred to as the "sequester", which were put into effect as part of the debt limit discussions last year as a stick to get Congress to act because the cuts were deemed so bad by both sides. It includes roughly $600 billion in cuts from the Defense budget and another $600 billion in cuts from discretionary (non-entitlement) domestic spending. So, importantly, Medicare, Medicaid and Social Security are largely unaffected.
The President has insisted that on the tax front, all tax rates remain the same for everyone making less than $250,000 a year, and that the tax rates on those making more than that (for married couples filing jointly), rates should return to their Clinton era levels. This would raise roughly $1.2 trillion dollars, and as a result Republicans have insisted in at least that amount being cut from spending programs. In what the President refers to as a "balanced approach" he has offered Congress between $800 billion (originally) and most recently $1.2 trillion in spending reductions that are from more palatable programs than the sequester would cut (this reduced the burden on Defense and included cuts to Medicare and tying Social Security cost of living adjustments to the Consumer Price Index so that they would go up slower). Republicans believe the President's cuts are not sufficient, and that due to accounting tricks, the offer was more in the neighborhood of $900 billion (not $1.2 trillion) in spending reductions and have rejected this offer.
House Speaker John Boehner countered with what he calls "Plan B". This only addressed the tax portion of the "fiscal cliff" leaving the sequester in place and would have left tax rates at their current levels for everyone making less than $1 million (rather than $250,000 like the President wants). This failed to pass the House last week because he could not get enough Republicans to vote for it (all Democrats would have voted against it as well).
On December 28th, the President offered a new plan, very similar to his original plan on taxes, but that would remove all the spending cuts and push out the deadline on the sequester potion between 60-90 days. There has yet to be a response on this effort by the Republicans in Congress.