An Environmental Defense Fund ad published in regional newspapers urged the Democrats -- whose 12th District includes portions of Richmond County -- to support the proposal.
A 30-second ad sponsored by Vote.Vet.org will soon begin airing and continue for a week on local cable stations.
The measure, backed by President Barack Obama, would limit the emissions of greenhouse gases and is intended to reduce reliance on fossil fuels.
Greenhouse gases widely are considered a major cause of global warming, which many scientists say may wreak worldwide ecological havoc.
The legislation also would promote renewable sources of energy, low-carbon fuels, electric vehicles and energy efficiency in buildings, appliances, transportation and industry.
The TV ad features Zach Choate, described by Vote.Vet.org as a Georgia veteran of the war in Iraq.
"It's crucial to our national security that we get off our dependence on foreign oil and towards clean energy," Choate says in the commercial. "Right now, billions in Middle East oil profits help fund terrorism."
The ad urges viewers to call Mr. Barrow and tell him to support the measure.
Mr. Barrow said Friday that he supports the president's goal of reducing greenhouse gas emissions, but was noncommittal on the legislation.
He noted that there are competing versions of the proposal.
"Although there are a lot of ideas on how to achieve that goal, we've not yet arrived at a consensus on exactly what any one program ought to look like," he said.
Mr. Barrow said he can't commit his support to anything until "all the pieces are in place."
"We have to make sure that we're not overloading an already weak economy by penalizing individuals," he said. "But it makes good sense for all of us to give positive incentives to folks who make smart choices about efficiency and the environment."
Most Republicans oppose the measure and say fees that would be imposed on industries that emit greenhouse gases would be passed on to the public.
Some foes of the measure say it would add hundreds of dollars a year to household utility bills and sink the economy deeper into recession.
Vote.Vet.org spokesman Eric Schmeltzer said the group doesn't plan to target congressman,Jack Kingston, a Georgia Republican.
Spokesman Chris Crawford said Mr. Kingston is against imposing fees on industries that emit greenhouse gases.