Under Section 3 of Article II, the President “may, on extraordinary Occasions, convene both Houses, or either of them…”
I think it would be hilarious if Obama called the House of Representatives back into session, and told them that they would remain in session until they passed a bill addressing the border crisis. No vacation for you, parliament of crazies!
And besides being hilarious, it would be a hell of a good idea. The President would be rubbing in the fact that Congress isn't doing its job, and he's the grownup who is telling them: no, you can't go play outside until you clean up your room! And this would get the sort of play in the news that would help it sink in with the American public that we have a responsible President, and a House of irresponsible children.
The Republicans would play into it perfectly, too, by throwing a huge tantrum.
Do it, Mr. President. Call the House back into session. Do it now.
UPDATE: As it turned out, the House stayed around until Friday night and passed an 'immigration' bill, though a better phrase to describe it would be "deportation bill."