Since the Congress is a coequal branch of government, would seem to me they could order the sgt at arms to take him into custody for being an illegal.
I was not explicit enough, since they are both illegals, the sgt at arms could take either or both into custody.
They could definitely get him on acts Treason which to me this certainly is. Inviting foreign invaders who assault our laws to be his guest of honor? Who knows, maybe tonight someone who has loves their country enough will do just that and end this nightmare. Wouldn’t that be something, the POTUS being arrested on national TV.