Cooperative federalism in the United States entails cooperation and collaboration between the federal government and the states. This can take place in general, as a matter of principle, but cooperative federalism usually operates systematically. Under cooperative federalism, the federal government might cooperate with the states to implement specific laws or policies, like the Affordable Care Act or the American Recovery and Reinvestment Act, but it might be less willing to collaborate with states on other projects, like foreign policy or border security. Cooperative federalism is more like a long-term relationship in which each party tries to give a little and get a little benefit, instead of a straightforward competition or tug-of-war.
The idea was popularized in the 1930s, when the Great Depression made it difficult for states to provide public services and regulatory oversight of their economies in the same way they did during the more profitable years of the late-nineteenth century. Most of them simply weren’t large enough or rich enough to cope with the financial dislocation caused by the collapse of the stock market and banking system. They didn’t have easy ways to increase the flow of money into their economies, so it was inevitable that cooperation with the federal government eventually became necessary. By the end of the decade, the federal government had institutionalized its cooperation with states in broad areas of the economy and society—for example, under the Works Progress Administration, the Social Security Administration, and other programs of what came to be called "the New Deal." That tradition of cooperation and collaboration continues today.
Not everyone in the United States likes cooperative federalism. People who believe that the federal government has grown too powerful, that it bullies states using its control of money, and that it is violating the spirit of the Constitution are opposed to cooperative federalism. They wish for a return to the government arrangements of the early United States, which were more in the spirit of the country’s founding and which were codified into law in the Supreme Court decision McCulloch v. Maryland. That arrangement is usually called Dual Federalism, and it envisions states and the federal government as equals in a competition for resources and power over citizens.
Theories of Federalism: A Reader by Dimitrios Karmis and Wayne Norman, eds.