You can kill the funding without the president (he can’t physically FORCE Congress to include funding) but dissolving the department would require a presidential signature and can’t be done till Obama’s replaced.
For example: We abolish the EPA .Yet there are still thousands of pages of marxist ,anti-capitalism enviromental laws like that species act or whatever. Someone or some agency has to do environmental impact studies etc. to enforce those laws, to make sure that no habitat of some insect or forest or whatever is “harmed” by a power plant or construction or factory etc.. Of course those are horrible laws but it is the President's duty to see that those laws are enforced.So these laws have to be repealed first.
Why don't people understand that it is laws that are the problem: case in point the 3000 page government socialist healthcare law just recently passed.