Taft's people wanted to extend federal ____________ regulations to New Mexico.

The correct answer highlights the efforts during Taft's administration to implement federal land use regulations in New Mexico. In the early 20th century, federal control over land management became increasingly important, especially in western states where large amounts of land were owned by the federal government. Implementing land use regulations aimed to standardize practices across states, including New Mexico, which was still experiencing growth and development.

Federal land use regulations were intended to manage resources, conserve the environment, and regulate land development to promote systematic growth. This was particularly relevant for New Mexico, which had vast areas of land that needed management to ensure sustainable development while balancing economic interests and environmental protection.

The other options pertain to different aspects of federal governance. Public road project regulations focus on transportation infrastructure rather than land management. Tariffs relate to trade and economic policy rather than the direct management of land resources. Railroad regulations, while significant in economic terms, do not align with the broader context of land management. Thus, the emphasis on extending federal land use regulations accurately reflects the policies considered during Taft's administration concerning the governance of New Mexico.