If you change your date to a future date, and then send a message, they will still receive it, but the date will have that future date. For example, you've all got my message saying Merry Christmas dated December 25, 2012, right?
The date range of the 3DS is January 1, 2000 to December 31, 2050. So if you want to do January 1, 2051, you have to set it to December 31, 2050 and wait until the clock goes past midnight (set it to 23:59:59 to make it quicker, obviously).