On Wednesday, former Secretary of State Jim Baker, still considered a power-player within the party and an old hand at getting things done in the halls of power, visited the White House to try to get President Donald Trump behind the plan.
So what exactly is the plan?
According to published reports, the proposal is to place a new tax on oil, coal and natural gas -- starting at $40 a ton and increasing over time -- and then use to proceeds to pay quarterly dividends to every American taxpayer.
Proponents of the plan say it would result in each taxpaying family of four receiving about $2,000 a year.
Baker and his allies believe a majority of taxpayers would get more money back than they would pay in increased fuel costs -- and that would be an incentive to embrace renewable energy and more fuel-efficient cars, hybrids and electric vehicles.
They estimate the plan would raise $200 billion to $300 billion annually.
But Baker and his allies also recommend repealing nearly all carbon emissions regulations approved under President Barack Obama, including the Clean Power Plan, and that troubles environmentalists.
In touting a plan, the senior Republicans are trying to convince the Trump administration to take a leadership role on fighting climate change -- a subject the new president has frequently expressed skepticism about.
In addition, Trump's pick to run the Environmental Protection Agency, Oklahoma Attorney General Scott Pruitt, is an outspoken climate-change denier.
Baker led a delegation of senior Republicans that met Wednesday with White House Chief of Staff Reince Priebus and Gary Cohn, director of the National Economic Council.
But even before the meeting, Baker said he knows getting the proposal enacted into policy will be tough in the current environment in Washington.
Congressional Republicans have repeatedly opposed the imposition of a carbon tax, which would raise the cost of fossil fuels to discourage consumption.
Last June, in fact, the Republican-lead House voted in favor of a resolution opposing carbon taxes.
The GOP contends such a tax would harm all Americans by raising the cost of food, gasoline and other essentials.
The White House has declined to comment on Wednesday's meeting.
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