I don't see how he can given the Constitution bestows that power upon the Congress:
Someone has to be the adult in this Republican inflicted crisis. The POTUS does have executive powers and the GOP would have to go to the Supreme Court and ask them to overturn those EO's. But until they do so they would be the "law of the land" irrespective of their constitutionality.
The point to remember is that Obama is looking to the long term future when he pointed out that he is considering the consequences of what Congress is doing will have on future presidents.
Even if the SCOTUS does overturn those EO's they will be violating their own pro-corporate position in favor of partisanship instead. Roberts has already demonstrated that he will abandon partisan "principle" in favor of corporate profits. So the odds are that the court will uphold those EO's given that the presidency does have executive power in a time of crisis.
If that is the outcome the Republicans will be devastated and this will have cost them far more than they will have gained. Granted this is all speculation on my part but I am going by most likely probabilities. Reality might turn out differently.