Final answer:
Presidents primarily use the strategy of going public to apply public pressure on Congress, using media to focus attention on issues, but also employ private negotiations to secure legislative achievements.
Step-by-step explanation:
When facing resistance in Congress, especially during times of increasing partisanship and when the president's party is in the minority, using the media and social media to draw attention can sway public opinion and pressure Congress. Presidents like Theodore Roosevelt have used the 'bully pulpit' approach to leverage their high approval ratings and the attention of the media to persuade the populace to push their representatives in Congress towards legislative action on issues important to the president.
In contrast, private negotiations also play a crucial role, with presidents often engaging in direct discussions with legislators or using legislative liaison officers to facilitate communication with Congress. They attempt to offer incentives and find common ground to build coalitions and secure legislative victories, a process that can be more subtle but effective in achieving policy goals. Presidents must weigh the benefits and pitfalls of going public, as it can sometimes polarize debate and make compromise more difficult, whereas private negotiations might allow for more nuanced and less confrontational solutions.