Under the plan the students are proposing, an initial tax of $40 per ton of carbon would be levied at the point where fossil fuels enter the economy, for instance a mine or port. The tax would increase over time. That money would then be returned to taxpayers in a per-person monthly payment, with half-payments going to children under the age of 18 and a limit of two children per family. The Climate Leadership Council created by Mr. Baker and Mr. Shultz estimates a dividend would amount to about $2,000 a year for a family of four.

As part of the deal, there would also be limitations on regulatory actions like the Clean Power Plan, which former President Barack Obama impose d to reduce carbon emissions from coal-fired power plants. Members of the coalition said they considered a promise to scale back future regulation key to encouraging Republican support.

Alexander Posner, 22, a Yale University senior who founded the group, said he has been interested in climate change and energy for years. When he read about the climate council Mr. Baker and Mr. Shultz began last year, he signed up for an internship . Soon after, he started contacting his peers at Republican clubs across the country to sound them out on creating a coalition of their own.

“We’ve had a lot of conversations, and literally not once has the validity of climate science come up,” Mr. Posner said. “I think students really want to have a solutions-based discussion.”

The coalition of 23 Republican student groups, five college Democratic clubs and three university environmental clubs comes at a unique moment of youth political activism. Students nationwide are mobilizing for gun control, inspired by the survivors of the school shooting in Parkland, Fla., and Mr. Posner said that, despite the profound differences in the two movements, young Republicans working on issues like climate change were watching the gun protests with interest.

“I think the common theme here is if representatives are not responding to the desires of their constituents, in particular young people,” he said, “then young people are going to step forward. This coalition on the climate front is sort of a reflecting of the inaction of adults.”

Last week the nonprofit Alliance for Market Solutions issued a survey on millennial attitudes toward climate change showing that nearly 60 percent of young Republicans acknowledge that human-induced climate change is real, and 88 percent of young Democrats . A majority of young people of both parties said they believed steps should be taken to slow or stop climate change.