In The Federalist No. 58, James Madison described the centrality of the power of the purse's role in the growth of representative government and its particular importance in the Constitution's governmental structure:

The House of Representatives cannot only refuse, but they alone can propose the supplies requisite for the support of the government. They, in a word, hold the purse--that powerful instrument by which we behold, in the history of the British Constitution, an infant and humble representation of the people gradually enlarging the sphere of its activity and importance, and finally reducing, as far as it seems to have wished, all the overgrown prerogatives of the other branches of government. This power over the purse may, in fact, be regarded as the most complete and effectual weapon with which any constitution can arm the immediate representatives of the people, for obtaining a redress of every grievance, and for carrying into effect every just and salutary measure.

Under the Articles of Confederation, under which Congress possessed the power to appropriate, there was no independent executive authority. With the creation of an executive under the Constitution, the Founders decided, in the words of Justice Joseph Story in Commentaries on the Constitution of the United States, "to preserve in full vigor the constitutional barrier between each department...that each should possess equally...the means of self-protection." An important means of self-protection for the legislative department was its ability to restrict the executive's access to public resources "but in Consequence of Appropriations made by Law." Justice Story continues:

And the [legislature] has, and must have, a controlling influence over the executive power, since it holds at its own command all the resources by which a chief magistrate could make himself formidable. It possesses the power over the purse of the nation and the property of the people. It can grant or withhold supplies; it can levy or withdraw taxes; it can unnerve the power of the sword by striking down the arm that wields it.

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If you don't hand the weapons to him he cannot use them.  The president cannot expend resources if congress does not allow it. No agency exists under our structure that forces your hand.  The Supreme court cannot compel the congress to release funds for previously authorized expenditures.  Indeed, the power of the the purse has been available to this congress, and it has not yet been exercised.  Your declaration of powerlessness was incorrect.

And the next time you want to explain how it works to me, perhaps you bring fluffy mittens.