As President Obama looks toward December's global conference on climate change in Copenhagen, conservatives are challenging a congressional budget estimate of the cost of the House energy bill.

House Democratic leaders said the bill that passed last week helped accomplish one of Obama's campaign promises and would make the U.S. a leader in international efforts to address climate change when negotiations take place in Copenhagen.

The legislation, totaling about 1,200 pages, would require the U.S. to reduce carbon dioxide and other greenhouse gas emissions by 17 percent from 2005 levels by 2020 and by 83 percent by mid-century.

But Ben Lieberman of the conservative-leaning Heritage Foundation, echoing the argument of other conservatives, says families will pay several thousand dollars more every year as a result of the bill.

"Each year down to 2050, the targets and timetables get more stringent," he told FOX News. "Just as the economy adjusts, the required reductions in energy go up."

Lieberman's prediction is close to 20 times what the Congressional Budget Office says it will cost to reduce the country's use of coal fired power plants, increase the fuel efficiency of cars and boost the use of renewable power sources.

But Jennifer Havercamp of the Environmental Defense Fund says Lieberman's estimate is way off the mark.

"We instituted a cap-and-trade system for acid rain just like the bill that passed the House, and the U.S. met its acid targets way earlier than we thought and at one third the cost," she said.

The House vote marked the first time either house of Congress has passed legislation to curb global warming gases. Ever since it passed, Obama has been working to get the measure passed in the Senate, where success will be tougher.

"The American people know that the nation that leads in building a 21st century, clean-energy economy is the nation that will lead in creating a 21st century global economy," he said.

The United Nation's climate chief says he's counting on Obama to convince China and India to limit the growth of their emissions. But India's environment minister said this week his country "will not accept any emission reduction target."

Senate Minority Leader Mitch McConnell says that's unacceptable.

"I don't think putting clamps on our economy when you know the Chinese and the Indians are not going to do it is a good idea," he said.

The House bill would force just a fraction of Europe's proposed cuts, and the president says it won't put clamps on the economy.

German Chancellor Angela Merkel said last week that Obama is 100 percent committed to reaching an agreement in Copenhagen and she suggested they also agree it should not be just a domestic economic calculation.

"It means that we take a commitment and shoulder a responsibility for those countries in the world that will be far more heavily affected by climate change," she said.

And yet the U.N.'s climate chief says the lesson he learned from the Kyoto accord is don't pass an agreement the Senate won't approve. And the Senate's likely to be quite pragmatic about what emerges from Copenhagen.

FOX News' Wendell Goler and The Associated Press contributed to this report.