The correct answers would be:
"To convince the public to support an idea" - Obviously, the president would like to have the support of the public on his plans.
"To encourage the public to unite" - It's ideal for a country to be united, focused on the goal of doing good for the country, as well as understanding the plans of the government, and being patient while they progress and start showing results.
"To motivate the public to take action" - This one is related to the previous one. Again he's motivating the public to get on board with his plan.