“It’s an ongoing question,” said Tim Phillips, the president of Americans for Prosperity, who said his organization was focused intently on the midterms. “But we don’t believe that we’re fully there yet as an organization.”

In a mark of the competition for the group’s favor, several top potential contenders for the Republican nomination interrupted their Labor Day weekends for a chance to court the donors and activists in Dallas, including Gov. Rick Perry of Texas, Senator Rand Paul of Kentucky and Gov. Mike Pence of Indiana. Gov. Chris Christie of New Jersey had a family obligation, an aide said, but pledged to headline a donor meeting that David Koch will host in New York next month. Senator Ted Cruz of Texas, beloved by Tea Party activists, was the featured speaker on Saturday afternoon.

“It would be a force multiplier for any Republican in the primary that is hard to rival,” Mr. Wilson said, “because they have these effective grass-roots organizations across the country, and they are learning how to be efficient and timely and targeted.”

On Thursday evening, Mr. Pence and Mr. Paul mingled with 140 top donors and Koch aides at a dinner hosted by David Koch, dining on Kansas City strip steaks and remarks by the conservative columnist George Will.

Mr. Paul has sought to convince the group’s libertarian-minded donors that his skepticism of foreign intervention makes him a better fit than other leading Republican candidates, most of whom share conservative views and records on fiscal issues.

“I don’t think it’s that far outside the traditional belief system of Republicans, but it does set me apart,” Mr. Paul said in an interview on Friday. “Americans don’t want a reckless and rash leader that takes them into war recklessly.”