As David noted yesterday, the figures Republicans are using to malign the cap-and-trade plan that Democrats put out this week are utterly, certifiably false. But that didn’t stop Minority Leader John Boehner (R-Ohio) from repeating them in yet another press release on Thursday.

“Families and small businesses are struggling to get by, but the Democrats’ budget would raise taxes on every American who drives a car, flips on a light switch, or buys a product manufactured in the United States,” says Boehner’s release. “In fact it would cost every family as much as $3,100 a year in additional energy costs through their ‘cap-and-trade’ energy tax, and will drive millions of good-paying American jobs overseas.”

Problem is, the $3,100 figure that Republicans are attributing to a 2007 MIT report is not backed up by the actual study. This has already been well-documented — PolitiFact researcher Alexander Lane called John Reilly, one of the report authors, and asked. And TPM got Reilly on the phone again to explain how the numbers got distorted.

On Wednesday, Reilly issued letters to Boehner and the Select Committee for Energy Independence and Global Warming clarifying what the study actually found and noting that Boehner’s figure “is nearly 10 times the correct estimate which is approximately $340.”

But this hasn’t stopped Boehner from repeating his claims. In fact, in today’s release he challenges Reilly on his own figures, and then invents justification by alleging — with nothing to back up his claim — that Democrats don’t intend to rebate money to consumers:

An MIT professor has questions about the $3,100 figure but his letter makes assumptions that are factually inaccurate. Moreover, he claims “government rebates to consumers” must be factored in. But we all know that Democrats have no intention of using a cap-and-trade system to deliver rebates to consumers; they want the tax revenue to fund more government spending.

The Democratic members of the Select Committee released their own rebuttal on Thursday detailing the distortions in the minority’s claims. “The Republican campaign to kill clean energy legislation uses the names of respected organizations like the Congressional Budget Office and the Massachusetts Institute of Technology, and then distorts their trusted analyses,” said the statement, issued by the office of committee chair Ed Markey (D-Mass.). “And while the Republicans are offering no real alternatives, this energy misinformation campaign assumes that no actual benefits will result from moving to a clean, energy efficient future or from reducing America’s dependence on foreign oil. It assumes American ingenuity and technological innovation are dead. It depends on recycling all the stale arguments and policies that have led to America’s dangerous dependence on foreign oil and harmed our national security.”