The most effective interpretation of President Roosevelt's speech in persuading Americans to support laws aimed at helping people during the Great Depression is that Roosevelt wants listeners to feel that the nation should do more to take care of people who need help.
In his address, Roosevelt highlights the struggle of a significant portion of the population who are "ill-housed, ill-clad, ill-nourished," which evokes feelings of empathy and urgency. By framing the test of progress in terms of how well the nation cares for its most vulnerable citizens, he appeals to the moral responsibility of individuals and the government. This emotional appeal encourages listeners to support measures that would provide aid to those in need, fostering a sense of collective action and responsibility towards less fortunate members of society.
While the other options touch on aspects of wealth and the president's authority, the primary persuasive element lies in Roosevelt’s call for compassion and action to help those who are suffering, which aligns with the overarching goal of his New Deal programs.