First, I suggest you take some time to read about JMP date, time functions and formats. It really will help you with the kinds of things you are looking to do. So taking what you asked for your first question in your response, you can use the informat() function to specify any particular date or date time for evaluation. So taking my last format and making it more specific, it would be:
If( :The Date < informat("09/23/2012", "m/d/y" ), 1, 2 );
If you want it to be down to an hour, minute, second, you just have to specify it, along with the JMP format that is required to read it.
For your analysis of one day vs. all other days, I would simply create a new column or a new transformation using the following formula
If( informat("09/23/2012 23:59:59", "m//d/y h:m:s") < :The Date <
informat( "09/24/2012", "m/d/y"), 1, 2 );
Jim