With a sweeping overhaul of the tax code on the horizon, two Senate Democrats believe this is the moment to broach the third rail of climate change policy: a carbon tax.

The plan by the senators, Sheldon Whitehouse of Rhode Island and Brian Schatz of Hawaii, to level a $49 per metric ton fee on greenhouse gas emissions is widely acknowledged as a long shot. But the lawmakers, along with climate activists and a cadre of conservative supporters, insist the tax reform is a way to create bipartisan support. The senators propose to use a portion of the estimated $2.1 trillion they anticipate in carbon tax revenue over the first 10 years to reduce the top marginal corporate tax income rate, something the White House has called for.

They also hope to have an ally in President Trump’s economic adviser, Gary D. Cohn, who met in February with a prominent group of Republicans advocating a similar plan.

No Republican lawmaker has signed on to the Senate measure. Mr. Trump, who routinely proclaims his affection for coal, during the presidential campaign flatly rejected via Twitter a suggestion that he might put a price on carbon pollution. The senators steering the effort admit they haven’t even broached a carbon tax directly with members of the administration, and the White House has distanced itself from the policy.