I wonder why there is such hair-splitting on the issue. As far as meaning goes, there will be no situation when the president is seen as different from his admin nor has the admin got powers sans the president’s sanction. So I do not see much difference among A, B and D.
However, you can see how horribly each of the choices distorts the original meaning.
1. Keep A, the original content.
2. B. It does not even mention the President. Whose admin is it anyway?
3. Does the pronoun
it stand for the package or the administration
His first year is totally missing from the context
4. What is the difference between
its budget reduction package and
the budget reduction passge in D?.
Its is good enough.
5. Why is the split between the President and the Administration in E?
Overall, I am afraid this topic takes us nowhere. If we ignore meaning , perhaps any choice other than C may be good enough as all seem to go by the copybook structure of the past subjunctive or the past conditional.