"How effective is Federalism when the majority of the states disagree with the Federal Government?" 
Local Governments Role in Federalism
Federalism is the division of power between national and local entities. In theory, federalism should produce policies tailored to individual states, taking into account individual perspectives that may vary based upon geography. With that in mind, an ideal federalist system should delegate a majority of policy decisions to local and state governments. In an attempt to preserve this power of the local government, the tenth amendment of the constitution was created stating, "The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people".
National Government Role in Federalism
Under a federalist system, the national government ideally has little power over enforcement of legislation. So what exactly should the national government be responsible for, and why have such an establishment if we are trying to delegate a lot of the power to the states? Within Section Eight of Article I in the U.S. constitution, powers of the national congress are explicitly laid out. These duties include: establishment of post offices, coining of money, borrow money on behalf of the country, raise and support armies, regulate commerce with foreign nations along with many others. All of these powers are things that individual states are unable to do on their own... they all provide structure for communication, trade, and defense between the states. The purpose of these powers delegated to the federal government is to band the states together and allow them to coexist under one common monetary, postal, and defense system. The intention was never for the federal government to rule over each of the states, creating policy to be enacted across the whole country. Today, the federalist ideals and principles stated in the constitution are not entirely adhered to as the power of the national government has been inflated beyond what was envisioned.
Federalism in Context
Though our system was founded on federalist principles, we do not get to really witness the effectiveness of federalism in the contemporary landscape of government and politics. State and local governments are now often overlooked. Congressional, executive, and judicial powers seem to be concentrated more in Washington D.C. than anywhere else in the country... this is not what the founders or what the authors of the Federalist papers would endorse. Real federalism dilutes the power of the central government by limiting their authority to only be able to preside over things that states are unable to regulate on their own. So, we are far removed from the federalist principles that are cited in our Constitution by the founders, but what if we were in such a system, what would the dynamic be between the states?
Response to Question
In such a federalist system, if the states were in disagreement with the national government, there would be limited things that the national government would be able to do to limit that. The beauty of such a system allows for diversity of policy throughout a nation, barring the federal government from infringing on the states while not considering the unique perspectives of each of them. So to answer the question posed: states are allowed to disagree with each other and with the central power in federalism... and it creates a product that is beneficial for all involved. Such disagreements are not a deficit of the system, but rather a feature. Citizens are able to have mobility and move within a nation to an area with policies that align with their goals and ideals. Similar to market forces, federalism provides a force of competition for state governments to attract residents, businesses, and investment.
