Hello Steven,
MCUXpresso SDK only supports the MK20Dxxx10 which runs at 100Mhz. Taking a look at the Teensy 3.1 it is running up to 72Mhz, so the SDK available will not work. However there is an article which explains what modifications you can do to allow for SWD debugging.
You can check that out here.
If you would like to work with one of our solutions I would recommend the following:
For a development board with a Cortex M4, the Freedom Development Board for Kinetis K64 is a very complete option.
If you would like to stick to something similar to the Teensy 3.1 you can check out the LPC845-BRK, but this one has an Cortex M0+ .
Both of these already have the debugger implemented as well as the SDK available and example projects so you will not have any trouble getting started with MCUXpresso IDE.
Let me know if this helps!
Sabina