It turns out that the answer is "YES", but the process isn't exactly easy. In fact the requirement of a size 0 Phillips screwdrivers alone tips us off that this isn't going to be easy or quick.

In fact Nintendo has made a video do show you the entire process in depth. First off you will need to gather the required stuff necessary to complete the process. Here is a list of what you will need: Your current 3DS/2DS and its SD Card, A New Nintendo 3DS XL and A microSD card of equal or larger capacity (a 4GB one comes installed in the New 3DS XL), A size 0 Phillips screwdriver, A computer, An adapter to connect the SD and MicroSD cards to said computer, and Wireless broadband internet access.

While Nintendo admits that you can transfer your data across the wireless, they estimate that would take about 4 hours to do. So using the computer is the best way to get the transfer done the fastest, but it requires you go through about 14 steps to get it done. Apparently there is no simply way to make this happen any easier.