Usually an SSR is AC only. It has a zero-crossing detection circuit so that it only switches on or off when the AC voltage crosses zero. DC doesn't, so it will never switch.
The datasheet on the Sparkfun site does show a possible part number for a DC version of that device. (Replace the last "A" in the part number with a "D") but I doubt that Sparkfun stocks that version. The big electronics houses such as Mouser, Farnell and Digi-Key will have hundreds of similar devices with the DC option.
A MOSFET is an option too but you will have to do a bit more work to connect wires to it and put it on a heatsink. It should not be too hard to find an appropriate device in this kind of simple 'relay' package.