In order for Congress or the President to act there must be a constitutional basis for that action. I direct your attention to United States v. Lopez, 514 U.S. 549 (1995). Layman's summary here:
The Supreme Court ruled that the Commerce Clause, which to that point had granted seemingly infinite power to Congress, did not extend a general police power. Lopez had violated an act of congress banning firearms in school zones. The law was ruled unconstitutional. Note that even the typical anti-gun "but its for the children!" argument fell on deaf ears. So in my mind, in light of Heller and Lopez, even if Obama could influence Congress to pass a law against concealed carry, it would be unconstitutional.
I think the thing to fear is the influence he would try to exert on state lawmakers. Like tying federal funds to the state's concealed carry laws.