Businesses have added 4.5 million workers under a new program that provides tax breaks for hiring unemployed workers, the Treasury Department said Monday.

It is unclear, however, how many of those workers would have been added without the tax break.

President Barack Obama signed a law in March that exempts businesses hiring people who have been unemployed for at least 60 days from paying the 6.2 percent Social Security payroll tax through December. Employers get an additional $1,000 credit if new workers stay on the job a full year.

Treasury released a report Monday estimating that from February to May, businesses added 4.5 million workers who qualify for the tax breaks. Those businesses are projected to save $8.5 billion in taxes.

"Targeted, temporary incentives like the HIRE Act are helping to fuel a private-sector-led recovery," said Alan Krueger, assistant Treasury secretary. "After a period of extraordinary difficulty, the economy is continuing to grow and private sector companies have added jobs for six straight months."

The report, however, does not estimate how many of those jobs would have been added without the tax break.

Nigel Gault, chief U.S. economist for IHS Global Insight, said, "Nobody knows how many of those 4.5 million would have been hired without the break."

"The bottom line is we just don't know," Gault said. It's going to require a lot more evidence before we can make any confident statements about how much impact the tax credit had."