Tax Cuts Are a Hit With One Pivotal G.O.P. Group: Rich Donors

A person close to the largest donor, Mr. Adelson, said that the billionaire did not discuss his savings on the tax bill in the context of his donations to the Congressional Leadership Fund. His contributions, the person said, were more a product of his broader political philosophy.

In some of its early ads, the super PAC has used voters in congressional districts to say how the tax cut has helped them. Mr. Bliss said he had “all but begged every campaign to run on the middle-class tax cut” — an appeal that so far has not often been heeded.

“It’s a central thematic,” he said. “In this environment, if you don’t make clear the contrasts between the two teams, then you are not going to get the benefit of the doubt.” Two who have, he said — Carlos Curbelo in Florida and Will Hurd in Texas — are doing better than many other incumbents who serve in districts won by Hillary Clinton in 2016.

Otherwise, the headwinds are strong. “Absolutely Democrats have more energy than we do,” he said.

The super PAC has field offices in 40 congressional districts around the country. Mr. Bliss said they had identified 50,000 to 70,000 voters in each of them, and began trying to persuade them more than a year ago with a regular campaign of door knocking, using a positive message in contrast to what voters see on television.

In Nebraska’s Second Congressional District, for instance, the super PAC has a target group of voters that it repeatedly reminds of the attention that Representative Don Bacon has paid to the preservation of Offutt Air Force Base, a major economic engine in the district, he said.

The group is also defying convention by airing television ads in more than a dozen districts in August, a time when many voters may not be paying attention to politics.

“This is a really tough environment,” Mr. Bliss said. “If you don’t win in August, you are not going to win in October.”