With unemployment at 8.2 percent, President Obama's claim today that "the private sector is doing fine" was off-key and ignited a rapid barrage of criticism from Republicans who said the president is out of touch with the country's economic problems.

But is the president correct? Are private companies "doing fine"?

Compared to the public sector, the private sector is growing substantially. In May, the government shed 13,000 jobs while private companies added 82,000 employees.

Over the past year the private sector has added nearly 2 million jobs and GDP has grown by 2 percent. According to Christopher Thornberg, an economist and co-founder of Beacon Economics, that is a "normal pace" for growth.

"Why it seems so painful is because we had that recession," Thornberg said. "We had the trough of the economy and then started growing at a normal pace. We haven't had that catch up."

The public sector, on the other hand, has cut 161,000 jobs over the past year, the vast of which came at the state and local level, where payrolls have decreased by 111,000 since May 2011.

"Where we're seeing weaknesses in our economy have to do with state and local government," Obama said at Friday's press conference.

The president attributed these state and local job cuts to falling tax revenues where caused states, cities and counties to make deep budget cuts that the federal government has not stepped in to help fill.

"I think that is undoubtedly true," said Ken Jacobs, the chairman of the University of California Berkeley's Center for Labor Research and Education.

And those disappearing government jobs are having a "real drag" on the economy, Jacobs said.

"Rather than being counter-cyclical," he said the government "becomes pro-cyclical, making things worse rather than making things better."

If the government had not parsed back payrolls, Jacobs said the unemployment rate would be below 8 percent and the private sector, stimulated by increased demand from the additional public employees, would be growing faster.

"The private sector is doing what it's supposed to do," he said. "By withdrawing demand, the public sector is effectively failing it."