Currently the system is whatever Obama wants he gets.
Check it out:

House Speaker John Boehner (R.-Ohio) said at a press conference this morning that President Barack Obama had no constitutional authority to take the unilateral action he has taken on immigration and that by doing so the president has posed a serious threat to the U.S. system of government.

Boehner, however, said that while House Republicans were “going to proceed” to counter the president’s action, they had not yet decided how they would proceed.