Final answer:
Presidents seek public support to ensure political legitimacy and influence, which is crucial for the success of their agenda. This support is strongest post-Inauguration and can be bolstered by a clear mandate from the electorate.
Step-by-step explanation:
The primary reason that presidents work tirelessly to win public support for their agenda is c) To garner political legitimacy and influence. Public opinion matters because it reinforces the president's political legitimacy and can lead to successful implementation of their policy goals. Immediately following Inauguration Day, presidents typically experience a surge in public approval, which they use to advance their agenda with greater ease. This support is even more significant when a president wins with a clear mandate, such as the majority of the popular vote, which was the case with Barack Obama in 2008.
High public approval allows presidents to use their position to influence media attention on crucial issues. While presidents have limited ability to shape public opinion, favorable conditions like party control of Congress or timely crises can help them move policies forward. Regardless, success is not guaranteed and often relies on the president's ability to negotiate and reach compromises out of the public eye.