Navin Nayak, the League of Conservation Voters's senior vice president of campaigns, likened the challenge Republicans face with young voters to the challenge they face with Hispanics.

The GOP has historically failed to win both demographic groups, and the party's deficit with Hispanics in particular — one of the nation's fastest-growing minority groups — was seen as dramatic enough to prompt the party to make passage of immigration reform a priority, to help Republicans appeal to Hispanic voters.

Nayak noted that the motivation for Republicans to take action on immigration reform largely lies in the harm it could do to the party's brand nationally.

"Individual members may not feel this pressure, but if the party continues to be branded as anti-immigrant it dramatically constrains their viability in key states and at the national level," he said.

He said that the party could face a similar problem with young voters if it doesn't begin to move forward on climate change.

"I think they face a similar challenge on our issue. I think there's a generation of young voters and even suburban moms that look at a Republican leadership right now that doesn't believe in science, and is increasingly wondering, 'Why would I ever support candidates who don't believe in science or are making decisions based solely on their ties to oil companies?'" he said.

President Obama took about 60 percent of the youth vote in 2012, and Republicans noted in a postmortem report that the party faces serious problems appealing to that demographic going forward.

Obama announced a major push for climate change legislation last week, much of which was panned by Republicans, who see it as an attack on the coal industry and charge it will raise energy prices and hurt job creation.