WASHINGTON — Americans for Prosperity — the group backed by David H. and Charles G. Koch that has been pouring millions of dollars into competitive Senate races to the rising alarm of Democrats — was also among the politically active groups on the ground in this month’s special House election on Florida’s Gulf Coast.

But its agenda had little to do with the fate of David Jolly, the Republican candidate who won that race. The group’s ground troops — including those who knocked on doors, ran phone banks and reached out through social media to gauge ways to motivate voters — were part of a much greater project, with a prize much larger than a congressional seat.

Americans for Prosperity turned the Florida contest into its personal electoral laboratory to fine-tune get-out-the-vote tools and messaging for future elections as it pursues its overarching goal of convincing Americans that big government is bad government.

As the group emerges as a dominant force in the 2014 midterm elections, spending up to 10 times as much as any major outside Democratic group so far, officials of the organization say their effort is not confined to hammering away at President Obama’s Affordable Care Act. They are also trying to present the law as a case study in government ineptitude to change the way voters think about the role of government for years to come.