Ryan is a Congress critter. You know that.
Congress critters do not claim that they can do such things just with executive power. Well, the Demoncrats do, but they violate the law if and when they do.
Wiki actually has a good article here -
http://en.wikipedia.org/wiki/United_States_federal_budget
The President will submit a budget but it is the responsibility of the Congress to authorize and appropriate funds, so the real power is with Congress.
Ryan knows that his proposals will have to be debated and agreed to by the Congress and though the power and influence of the Executive is there, it will take a great amount of compromise to have it come to pass. Why say it will come out only one way, when there are likely hundreds of ways it may come to pass?
Think about it, no Democrat has voted for Obama's budgets because they are pure fantasy, useful only for talking points in debates and political speeches. But the Demoncrats have selectively passed extraordinarily expensive legislation despite that.
The Congress critters do a tremendous amount of horse trading to come up with funding, and the obstinacy of Reid in refusing to bring any House Republican passed budget to a vote has effectively ended any possibility of compromise. Hence the need for a Republican Congress, as well as Romney and Ryan in executive office, to get what needs to be done passed.