When it comes to routine government activities, such as immigration, justice, social welfare provision and climate change, many people believe that the US federal government operates slowly. One potential solution to increase the productivity and efficiency of the federal government is to adopt AI technologies and devices. AI technologies and devices already provide unique capabilities, services, and products, as demonstrated by smart homes, autonomous vehicles, delivery drones, GPS navigation, and virtual assistants such as Amazon's Alexa. However, incorporating massive AI into the US federal government would present several challenges, including ethical and legal concerns, outdated infrastructure, unprepared human capital, institutional obstacles, and a lack of social acceptance. How can US policymakers promote policies that increase AI usage in the face of these challenges? This will require a comprehensive strategy at the intersection of science, policy, and economics that addresses the aforementioned challenges. In this paper, we survey literature on the interrelated policy process to understand the advancement, or lack thereof, of AI in the US federal government, an emerging area of interest. To accomplish this, we examine several policy process frameworks, including the Advocacy Coalition Framework (ACF), Multiple Streams Approach (MSA), Punctuated Equilibrium Theory, Internal Determinants and Diffusion (ID&D), Narrative Policy Framework (NPF), and Institutional Analysis and Development (IAD). We hope that insights from this literature will identify a set of policies to promote AI-operated functionalities in the US federal government.