Well, the punch line wouldn't make much difference. I mean, the guy entered the fenced area of the White House, wandered around awhile (apparently), and rode alone with the President in an elevator. Doesn't that make Secret Service look like a bunch of clowns? Now, the cartoonist shows the intruder having a high old time in the tub while the Pres is brushing his teeth. That's pretty much the whole joke, but the punch line has the guy casually offering inconsequential advice to an apparently very startled Obama.
The whole idea seems to be commentary on the failure of the Secret Service's ability to protect the President. It would probably would have worked without any caption at all. Whether the intent was racial or not, I've no idea.