The 195,000 gain in June non-farm payrolls announced Friday doesn't erase the weakness of the U.S. labor market, said Diana Furchtgott-Roth, former chief-of-staff of President George W. Bush’s Council of Economic Advisors.

Job growth is steady, but it's slow, averaging 196,000 over the last three months, she told Newsmax TV in an exclusive interview.

"It's not enough to get down the backlog of jobs from the recession," said Furchtgott-Roth, now a senior fellow at the Manhattan Institute. "So we're still about 2.4 million jobs lower than in December 2007, when the recession started."

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With 110,000 to 120,000 new entrants to the labor force each month, "it's going to take a while at the rate of 190,000 [new hires] a month to get that 2.5 million backlog down."

While the standard measure of unemployment was unchanged at 7.6 percent in June, the broadest measure soared to 14.3 percent from 13.8 percent in May, Furchtgott-Roth notes. That includes people who have given up looking for work and those working part-time who want to work full time.

There were 322,000 part-timers who wanted to be full-timers in June, she said. That's largely because when the Affordable Care Act kicks in, businesses with at least 50 employees working at least 30 hours a week must provide health insurance to them or face a penalty, she said. 

While that requirement was put off for a year (until 2015) this week, "it is having very real effects," Furchtgott-Roth said.

When it comes to the Federal Reserve, the stronger-than-expected June payroll gain, along with upward revisions for April and May, "might make the Fed think that the economy is doing a little bit better," Furchtgott-Roth said.

"Certainly the labor market is doing better than was previously thought, so it might lead them to taper off QE3 [quantitative easing]."

So what happens to financial markets when the Fed finally does "pull back the punchbowl?"

Interest rates will rise, Furchtgott-Roth said. And "a lot of these people who’ve been looking for high yields in the stock market are going to go back to safer investments with just higher interest rates," she said. "They’re going to go back to bonds."

Then it's up to Congress to take over from the Fed in boosting the economy, Furchtgott-Roth said. "There are things they could do, like lowering corporate tax rates. Our corporate tax rate right now is 35 percent. The OECD [Organization for Economic Cooperation and Development] average is 24 percent."

The government should scrap the employer health insurance mandate, she said. "It’s just amazing that five years ago, a company could move from 49 to 50 employees without penalty. They could hire someone 35 hours, 40 hours without fear of any penalty," Furchtgott-Roth said.

"The fact they can’t do that now is dampening hiring."

As for the economy's path for the summer, that's difficult to predict, she said. "On the one hand, consumer spending could go on rising, but on the other hand interest rates have gone up a little bit."