The first paragraph gives an insight about this.
President Barack Obama traveled to California on Friday to highlight the state’s drought emergency at two events near Fresno, calling for shared sacrifice to help manage the state’s worst water shortage in decades. He then spent the rest of the weekend enjoying the hospitality of some of the state’s top water hogs: desert golf courses.
It's probably a tongue-in-cheek comment by RNC spokeswoman Kirsten Kukowski. Check out the meaning of the words used here:
soapbox (without space) - A platform raised above the surrounding level to give prominence to the person on it.
tee box - Starting point where a golfer puts a ball into play for a hole.
In this context, it means that the president simply did both - political work by addressing the 'water shortage issue' but (then) also playing golf on the ground that requires 'too much water' to maintain.