Immediately, the New Deal was a terrible idea that prolonged the Depression but years. I'll provide a brief explanation to qualify this answer.
All economic depressions are the result of deflation in the value of particular assets, usually most severely in whatever assets were over-valued, with an accompanying deflation in most other assets and, in most cases, an rise in the value of the denominated currency. Deflation is a necessary corrective mechanism in capitalist economies by which excess, non-backed credit (credit emitted for speculative rather than productive enterprise, with virtually no chance of principal repayment) is cleared from the system through write-offs and bankruptcy.
Now, GDP, which is the metric by which depressions are recognized, is appropriately define as:
GDP = C + I + G + (x - i)
C is consumption, I is investment, G is government expenditure, and (x - i) is net exports, that is the money gained from export less the money spent on import. The New Deal sought, as do the economic policies of the current and immediately previous administrations, to increase G to offset the contraction in the other terms. The problem is that the government itself, both then and now, has little to now inherent wealth. All government expenditure must come from either the levying and payment of taxes, or deficit borrowing. A depression means a reduction in C, I and (usually) net exports (consumption is decreased because of a lack of disposable income, I because there are few attractive investment opportunities, and net exports because often in the periods preceding depressions, producers of real goods borrow beyond their means to sustain high growth, and are then rendered insovlent). This means that tax receipts are decimated (a fact that was and is being borne out in the current depression) and the government, should it choose to try and shoulder the economic system, must deficit spend. That is how you ending with the 1.1 - 1.4 trillion deficit each year for the past three years, and will again this year.
Worse that the immediate fiscal problems, the New Deal formally ushered in the welfare state in which the American people currently languish. Such behavior will continue inexorably, as the inherent naturalist and anti-Catholic spirit of the United States and its Constitution, means that its corruption and dissolution were a forgone conclusion more than two centuries ago.