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Health and Human Services Secretary Tom Price argued Sunday that more Americans would have insurance under the Senate Republicans’ new health care bill, compared to the 2010 ObamaCare law they've been trying to replace. But the Congressional Budget Office analysis of the bill, which would project those coverage numbers, will not be released Monday as anticipated.

“One of the interesting things that's in this bill ... is the opportunity to make certain that those folks that actually fell into a gap below 100 percent of the poverty level, but above where a state might allow individuals on the Medicaid system... this bill provides for coverage for those individuals through the tax credit process," Price said on Fox News’ “Sunday Morning Futures.” “That hole was not covered before.”

He suggested that tax credits in the new bill would in part help those who had previously fallen into that coverage gap.

“That’s something that’s new,” said Price, a doctor. “That also is one of the reasons that we believe we’re going to be able to cover more individuals on this bill than are currently covered.”

Senate Majority Leader Mitch McConnell, R-Ky., was expected to hold a key vote this week on the overhaul bill.

But the nonpartisan CBO apparently slowed its efforts to make that deadline after McConnell delayed the vote until Arizona GOP Sen. John McCain can return to Washington. He underwent surgery last Friday to removal a blood clot behind one eye and is expected to be gone at least a week.

The CBO’s analysis of Senate Republicans’ first ObamaCare overhaul bill this year -- released before Congress’ July 4 recess but which lacked enough support to even get a vote -- concluded 22 million more Americans would be uninsured, compared to ObamaCare.

Price and other Washington Republicans have argued that CBO projections are not exact and that the office was off on its ObamaCare numbers, too.

“CBO doesn’t even capture those individuals who say to the federal government, ‘I don’t want the plan that you think I need. I want the plan that I know I need for myself and for my family.’ So those numbers are so flawed in terms of what actually happens in the real world,” Price said.

Price also said he recently returned from the annual National Governors Association meeting where state leaders said they want the overhaul bill to have “flexibility” to designing a Medicaid program “for their own population” and want it to include adequate resources to insure the “vulnerable population.”