Final answer:
The President can affect Federal Court decisions by nominating judges, influencing cases through the Solicitor General, submitting amicus briefs, and overseeing implementation and enforcement of court decisions. If finding decisions unjust, the President's options include legislative advocacy, future nominations, or swaying public opinion.
Step-by-step explanation:
The President of the United States has several ways to directly affect the decisions of the Federal Court System. One significant way is through the power to nominate federal judges, including those on the U.S. Supreme Court, who serve lifetime appointments, thus leaving a lasting imprint on the judiciary. The President also has influence through the U.S. Solicitor General who represents the government in the Supreme Court and by submitting amicus briefs in cases where the U.S. is not a party but still has an interest. Furthermore, the president works within a system of checks and balances, where the Court relies on the executive branch for the implementation and enforcement of its decisions. If the President feels the courts are unjust, options are more restricted; he may choose to advocate for legislative change, seek to appoint new judges that align with his views when vacancies arise, or use the platform of the presidency to influence public opinion.