Rep. Alexandria Ocasio-Cortez's Green New Deal is garnering significant support, but the head of Exxon Mobil says people's views may change as the plan becomes more detailed and Americans begin to comprehend how it could affect their daily lives.

Ocasio-Cortez updated her blueprint for the Green New Deal last month, but has yet to suggest policies to achieve the plan's ambitious goals. Among other things, the freshman congresswoman calls for generating 100 percent of U.S. power from renewable sources, swapping gas-powered cars for electric vehicles and slashing carbon emissions — all in just 10 years.

Several Democratic presidential candidates have backed the plan, and the broad idea drew support across the political spectrum in a poll conducted last fall by public opinion researchers at Yale and George Mason University.

But eventually those big ideas will require action, says Exxon Chairman and CEO Darren Woods, and that's when the tide of public opinion could begin to turn against the Green New Deal.

"Energy is such an important part of people's daily lives and their standards of living that as you think about these big ideas and translate them down to smaller practical steps you take, people become very cognizant of what the impacts are for individuals," Woods said in an interview Wednesday with CNBC's Becky Quick. The interview aired Thursday on "Squawk Box."

"And as that starts to happen, I think people's view change as to how far they can go and how quickly they can go."

To be sure, as the world's largest publicly traded oil company, Exxon is not a disinterested party. The Green New Deal would almost certainly disrupt its business if it were successfully implemented.