The American welfare state is financed primarily by exactions on employers and employees. This has the following results: first, it artificially drives up the cost of labor, and thus encourages offshoring and automation; and second, it imposes costs that should logically be borne by all of society on a relatively small group of people.
The biggest problem with changing the system is breaking the relationship between payments and benefits on an individual basis. For that reason, some form of the payroll tax is bound to endure. It could be cut and replaced in large part by a VAT or a carbon tax, however.