The issue arises because Morning Edition decided to lead off its top of the hour news segment by telling listeners of the number of days until we hit the "fiscal cliff." While one could view this as a random fact, like the number of days until the winter solstice or Super Bowl XLVII, but that is presumably not how it was intended. Most likely this number would be viewed as a countdown against an important deadline.
Of course the end of the year is not an important deadline as every budget expert knows. If there is no deal by the end of the year, we will be subject to a higher rate of tax withholding come January 1, 2013. Since most of us will not get a paycheck on New Year's Day, we will not be immediately affected by the higher rate of withholding. We would only see an impact when we got our first paycheck of the year in the middle or the end of the month. If Congress and the President work out a deal before that point, there will be no increase in withholding.
Even if a deal is not reached in time to affect the first paycheck, if they come to an agreement later in the month, the extra withholding can be paid back in the second or third paycheck. This is likely to have a minimal impact on the economy, since most people will not change their spending patterns if they expect to get any extra withholding refunded in the near future. For people literally living paycheck to paycheck the extra withholding will be a hardship, but the impact on the economy will be minimal.
There is a similar story with government spending. If it looks like a deal will be reached, President Obama need not adjust the flow of spending at all in January.
For these reasons, there is no special importance to the January 1 deadline. There are of course many political figures, such as the corporate CEOs in the Campaign to Fix the Debt, who are trying to create a crisis atmosphere in order to force an early deal. They hope that this crisis atmosphere can create an environment in which hugely unpopular actions, like cutting Social Security and Medicare, will be possible.
If people at NPR want to support this political effort then they should do it in explicitly labeled commentary. They should not hijack the news section to advance their political agenda.