The remaining revenue would fund $500 billion in matching benefits for Social Security recipients, veteran's programs beneficiaries and other retirees. The last $100 billion would go toward block grants to fund benefits for miners in coal country or coastal protection in seaside areas.
It's uncertain whether a benefits program for miners would appeal to Trump. Against strong evidence to the contrary, Trump has long argued that the coal industry can stage a comeback. Instead of devising a safety net for miners, he has put his efforts into promoting U.S. coal exports and repealing Obama-era regulations.
The Climate Leadership Council's plan is similar, but would pay all carbon tax revenue directly to Americans. They suggest a monthly dividend that would add up to about $2,000 in the first year for a family of four. Authors on the study, "The Conservative Case for Carbon Dividends," include Republican former Cabinet members James Baker III and George Shultz.
They put forward a starting fee on companies of $40 per ton of carbon dioxide emitted and include measures to further cut regulations.
Many businesses support a carbon tax, at least in part because it offers clarity on the costs they will face in the future. Major multinational companies, including Exxon Mobil, BP and General Motors, are members of the Climate Leadership Council.
Whitehouse told the conservative American Enterprise Institute he was open to reviewing rules that could become unnecessary if Congress passes a carbon tax.
"Senator Schatz and I extend an open hand and olive limb. Find Senator Schatz and me a Republican to negotiate with. Then let's talk about the economics. Let's talk about the revenue," he said.
Both plans would impose a cost on energy-intensive goods — those that cause pollution in the process of being manufactured — when they're imported from countries that do not put a price on carbon emissions, or have weak systems. That potentially plays into Trump's tendency toward protectionist policies.
Baker and others presented the plan in February to Gary Cohn, the director of the National Economic Council, who is taking the lead on Trump's tax effort along with Treasury Secretary Steven Mnuchin. The Climate Leadership Council has scheduled meetings on Capitol Hill to push its plan, according to Sigal.
Whitehouse and Schatz also plan this fall to highlight the potential of a carbon fee to lower tax rates without "exploding the deficit," said Rich Davidson, deputy communications director for Whitehouse.
"When the carbon fee crosses a threshold of real possibility, it will attract support from groups that will enjoy lower rates, as well as those who see it as a last best hope against climate calamity," he told CNBC.