A proposed carbon tax also failed recently in a ballot initiative in Washington state, in part because it divided the left - with many liberals wanting to use any revenue to invest in clean energy and other social causes rather than to return it to the public.
Baker and his colleagues met Gary Cohn, the head of Trump's National Economic Council, as well as speaking more briefly with White House chief of staff Reince Priebus and counsellor to the president Kellyanne Conway.
A White House official said in an email it would be premature to conclude that the Administration was embracing the idea of a carbon tax.
"Secretary Baker is obviously a distinguished public servant with a wealth of experience," the official said. "This morning is one of many listening meetings the Administration is having with experts on a variety of issues and does not represent any eventual policy decision one way or the other."
The Vice-President's spokesman, Marc Lotter, said in an email that Baker had requested the meeting when they ran into each other "at the Super Bowl ... The Secretary mentioned going to the White House and the Vice-President asked him to pop by his office while he is here."
As for how the idea would be received politically, Baker said, "I have no idea but it is a good proposal, it's simple, it's conservative, it's free market, it's limited government."
Other supporters of the group's proposal include Ted Halstead, who founded the Climate Leadership Council and previously the New America Foundation, Rob Walton, the former chairman of the board of Walmart, and Thomas Stevenson, a US ambassador to Portugal under George W. Bush.
The revenue-neutral "carbon fee and dividend" idea, as it is sometimes called, has been popular among economists, including conservative ones, for years. It has also been strongly embraced by some leading climate scientists, such as former Nasa researcher James Hansen, and such advocacy groups as Citizens' Climate Lobby. But never before have major Republican statesmen from past administrations aligned behind it as publicly as they're doing now.
Baker and his colleagues estimate that the average family of four would receive US$2000 annually in dividends from the fee if it starts at US$40 per tonne - hard to see why that wouldn't be popular - and as the tax rises, so would their dividends. This would naturally create a constituency for ever-tougher climate change action.
They also assert that the proposal would be fundamentally progressive, because everyone would receive the same amount of revenue from the tax regardless of their income level, meaning that as a percentage, the new source of income would make much more of a difference for poorer people than for wealthier ones.
Finally, they suggest it's a needed compromise. "We have a regulatory left and a deregulatory right that are far, far apart," said Mankiw. "Both should acknowledge they're not going to have control forever."