Final answer:
The Social Security Act established the principle of federal responsibility for social welfare and created the basic framework of the welfare system.
Step-by-step explanation:
The piece of New Deal legislation that established the principle of federal responsibility for social welfare and created the basic framework of the welfare system was the Social Security Act. This act, signed into law in 1935, provided old-age pensions for retired workers and their dependents, unemployment insurance, financial compensation for injured workers, and direct financial aid for impoverished families with children. It was financed through taxes paid by employers and employees and also provided matching federal grants for states to create their own welfare programs.