Final answer:
Woodrow Wilson disregarded his health to appeal to the American people because he thought public backing for his policies, particularly for the League of Nations and his foreign policy agenda, was vitally important, even at the cost of his own well-being.
Step-by-step explanation:
President Woodrow Wilson disregarded his health and appealed strenuously to the American people because c) he believed it was crucial to gain public backing for his policies.
Wilson faced obstacles such as a divided nation on the issue of entering World War I, the challenge of securing reelection amidst neutrality and war preparedness campaigns, and significant opposition to the establishment of the League of Nations.
Despite the political pressures and his own debilitating stroke, Wilson prioritized securing the public's support for his foreign policy agenda, including the League of Nations, even to the detriment of his health.
Wilson embarked on a strenuous speaking tour across the country to build public support, which ultimately led to his health decline.
His relentless campaign aimed to create a consensus among Americans and pressure the Senate to support the treaty that encompassed the League of Nations, reflecting his conviction of the importance of public approval for his visionary policies.