Final answer:
The primary factor beyond nominee selection and ballot reform that influenced the erosion of party organizations' control over elections is media influence. The media's role as kingmakers and the shift towards candidate-centered campaigns have contributed to this erosion. The national level of party organization plays the most crucial role in presidential elections.
Step-by-step explanation:
The erosion of party organizations' control over government jobs and elections has been influenced by a variety of factors. Key among these is changes in nominee selection, which has shifted toward more open and voter-controlled primary systems. This change, alongside ballot reform, has contributed to a decrease in party influence. However, when it comes to the additional factor that has influenced this erosion, the answer is C) Media influence. The rise of media has been significant in shaping public opinion and individual priorities, which in turn affects public policy. Media coverage plays a critical role in elections, particularly after the McGovern-Fraser reforms of 1972, which led to party leaders no longer handpicking presidential candidates. Instead, the media have become increasingly influential as kingmakers in the political process.
Furthermore, campaigns have become more candidate-centered, with candidates often relying less on party support and more on their own resources and direct appeals to voters. Third parties typically have a limited impact on U.S. elections but can influence the political conversation and policy. Political parties attempt to maintain their grip on power sometimes by colluding with state and local governments, which could include measures that make it harder for new parties to rise.
The level of party organization most responsible for helping a party's nominee win the presidency is D) National. This level coordinates the broader election strategy and marshals resources across state lines to support their candidates.