Depending on the SSD, currently the maximum consumption (during a write) is ~17watts, or about 3 amps.
These spikes aren't sustained long, though, so you possibly could get away with a 2amp power supply and some...
Usually does. Many people don't realize that you are trying to supply power to two things plugged into one USB port, and it may have a 500mA limit of current.
After traveling down a long usb cable, power kind of ends...