Christmas to New Years: Huge crowds. One of the three most crowded weeks of the year (the other two are the week leading up to Easter and the one that starts with Easter). MK often closes to new entries because crowd is at capacity. Stand-by lines for popular rides run 2 hours and can get to three for Test Track and Soarin and that is all day except first thing in the morning. Fast passes for entire day run out for popular rides by 11:30. If you do not make restaurant ressies well in advance, you don't eat. Those high points reflect huge demand and huge crowds.
Early January: it depends on when Jan 1 falls. For 2008 it is likely, since it is on a Tuesday, that the entire week until the 6th will be almost as crowded as Christmas week because many, many schools will still be on break that week. When it falls on a Thursday, Friday, Saturday, or Sunday, the crowds start diminishing Monday after (because most schools go back in session on Monday or Tuesday) and are essentially gone by Tuesday.
After that initial few to more days in January, crowds are very manageable (think less than that November trip) except it gets crowded around the Martin Luther King holiday and somewhat crowded, but not really bad in the parks, during the Marathon weekend (usually the second weekend in January).