Final answer:
Carrie Chapman Catt led NAWSA in promoting women's suffrage by linking the right to vote to women's traditional roles as family caretakers, which assisted in gaining support and achieving some legislative victories.
Step-by-step explanation:
Under Carrie Chapman Catt's leadership, the National American Woman Suffrage Association (NAWSA) used a nuanced strategy to promote women's suffrage. Catt steered the organization to argue that enfranchisement would enable women to better perform their roles as caretakers of the family, by having a say on issues like public health and education. This approach linked the fight for suffrage with traditional gender roles and proved effective in both gaining support and achieving legislative successes. NAWSA also employed modern marketing techniques and political pressure to push for a federal amendment to the U.S. Constitution.
This shift in narrative from a demand for equality to a more pragmatic approach based on societal roles of women was one of the strategies that helped tilt public and legislative opinion in favor of the suffrage cause, particularly demonstrated in the success of suffrage gains in the western United States.