Aw, now I'm blushing.
So if the President has the statutory authority to do the exact opposite of the law, what is the point of having laws? Existing law states that people illegally entering the country are to be deported; Obama is directing the government to welcome and "integrate" them, the exact opposite. Are there any laws you believe the President has no authority to overturn?
This is blatantly the rule of man replacing the rule of law. I realize you can justify this to yourself, but imagine a President Cruz directing the federal government to eliminate gay marriage or fine owners of automobiles failing to produce more emissions than allowed. I suppose a dictatorship which periodically swings the other way (assuming this action doesn't buy Obama enough new voters to make us a one party nation) beats most dictatorships, but it certainly doesn't beat a republic ruled by laws.
If you can't imagine that, then imagine this: Even if Obama's maneuver presents the Democrats with a permanent majority, nature abhors a vacuum. How long do you feel Spanish-speaking immigrants will be satisfied with the Democrats' largesse before they begin competing directly for power?
Unless it is specifically labeled an Executive Order and numbered, signing it will not make it one. (Although as IronWing points out, that argument can be made.)
It would actually be easier for the Pubbies if Obama had signed an Executive Order; that can be quite simply repealed. Now they have to fight each action taken, or else impeach him. And if they impeach, they'll never convict, much less remove.