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On the basis of the Constitution and traditional legislative prerogatives, Congress lays claim to exclusive control over the purse. Nevertheless, while it is up to Congress to appropriate funds, it is also true that the President and the executive branch enjoy considerable discretion as to how those funds are spent. Existing studies tell us how the President formulates the budget and how Congress acts on the budget requests he submits. Surprisingly, we know relatively little about how the money, once appropriated, is actually spent. A notable exception in this field is a work by Lucius Wilmerding, Jr., published three decades ago.

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Yet another paper on the topic

Scholars disagree on the extent to which Congress may use appropriations limitations to control the President’s exercise of discretion in carrying out his or her duty to “execute the law,” especially in the area of national security—though all agree that Congress may not, under the guise of exercising its “power of the purse,” interfere with indispensable executive (or judicial) functions. Nor may the President frustrate congressional mandates by refusing to spend directed funds.

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My point is, that it is not clear that your statement is necessarily correct. It remains quite unclear as to what powers the President has in directing funds, especially when national security is in question. We do know that Homeland security gives him power to erect walls to thwart drug smuggling for example.