Obamacare's jobs diagnosis: What does the data say?

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The White House message on the Affordable Care Act has been consistent since the law's inception in 2010: Obamacare will be simple and economical.

"The data reflects that there is no support for the proposition that businesses are not hiring full-time employees because of the Affordable Care Act," White House Press Secretary Jay Carney said Tuesday.

But does the latest data tell a different story?

In a new survey of 300 accounting professionals, 66 percent say they expect the Affordable Care Act will make it less likely that businesses will add new employees in the next year. The survey, conducted by financial information company Sageworks, said only two percent are more likely to add new employees.

"The recent delay in the implementation of the Affordable Care Act, and the uncertainty that accompanies such a delay, won't help the employment situation," said Sageworks Chairman Brian Hamilton. "Private businesses are trying to map out their hiring and investment plans for the next twelve months, and a last minute delay like this will increase the likelihood that companies remain on the fence about hiring."

(Watch: Employers prepped for ACA before delay)

In fact, health care is now the top concern for small businesses according to the U.S. Chamber of Commerce's latest quarterly small business survey.

The survey, conducted by Harris Interactive in July 2013 among more than 1,3000 small business executives, found 71 percent of small businesses say the health care law makes it harder to hire. Only 30 percent say they are prepared to meet the requirements of the law, including participation in the marketplaces.

Critics of Obamacare further point to June's jump in the underemployment rate, from 13.8 percent to 14.3 percent, as an indication that businesses are hiring more part-time workers to avoid the mandate.

(Read More: Why Underemployment May Be Worse Than It Looks)

"We saw in the June jobs report the soft under-belly in employment is that the number of people who have part-time work, but who want full-time work, is going up," said Sara Fagen, a former senior aide to President George W. Bush.

Fagen said the health premiums in her company, DDC Advocacy, were up 23 percent this year, making it more difficult to hire workers.

Still, supporters of the Affordable Care Act say the bottom line is that Americans will no longer have to rely on their employers for quality insurance.

"Most of those people who aren't insured now will get insurance that is not dependent on their employment, and that's going to make a very big difference," said Former Vermont Governor Howard Dean, author of "Howard Dean's Prescription for Real Healthcare Reform."

"There are going to be some significant problems getting it up and running, but I do think it's going to work," he said.

—By CNBC Associate Producer Elizabeth Schulze. Follow her on Twitter@ESchulze9.