Does the president or Congress have more influence over policymaking by the bureaucracy? Despite a wealth of theoretical guidance, progress on this important question has proven elusive due to competing theoretical predictions and severe difficulties in measuring agency influence and oversight. We use a survey of federal executives to assess political influence, congressional oversight, and the policy preferences of agencies, committees, and the president on a comparable scale. Analyzing variation in political influence across and within agencies reveals that Congress is less influential relative to the White House when more committees are involved. While increasing the number of involved committees may maximize the electoral benefits for members, it may also undercut the ability of Congress as an institution to collectively respond to the actions of the presidency or the bureaucracy.