Libre, reflecting the Koch brothers’ views, supports a broad overhaul of the immigration system, including a path to citizenship. It waged a campaign in support of the Senate’s 2013 immigration effort, including airing in excess of $1 million in television ads. Those positions have put the group at odds with many of the party’s grass-roots conservative voters.

But the group has also drawn the ire of some Hispanic and immigration advocacy groups by raising concerns about some of President Obama’s more sweeping executive actions on immigration, and by pouring money into House races to help defeat two Hispanic lawmakers — Pete P. Gallego of Texas and Joe Garcia of Florida, both Democrats — because they supported the president’s health care plan, among other issues Libre opposes.

Craig Hughes, a Democratic strategist who managed Mr. Obama’s 2008 and 2012 campaigns in Colorado along with Senator Michael Bennet’s 2010 race there, said that while the group’s “potentially unlimited funds” from the Koch network were a source of worry for him, he thought the group would still have a tough time making its pitch to Hispanic voters.

“The question is, does an aggressive outreach and relationship-building program help them when their candidates are at such odds with the population?” Mr. Hughes said. “I am highly doubtful, but I never underestimate the impact of a massive amount of money in politics.”