Health and Human Services Secretary Tom Price said his administration doesn't have great faith in the Congressional Budget Office estimates of people who would no longer have health insurance under the Senate GOP's healthcare bill.

Last Monday, the CBO's analysis of the bill under consideration by the Senate said 22 million more people would become uninsured over a decade.

"The budget office does a pretty good job usually of saying what something is going to cost," Price said to "Fox News Sunday" host Brit Hume. "They've been woefully inadequate in being able to predict what kind of coverage. For example, they said, the Congressional Budget Office said that right now Obamacare would cover about 23-24 million people, and fact it's about 10 million people."

"We believe they are off by a huge factor here as well because they don't give any credit for individuals purchasing some type of insurance that the CBO says isn't credible insurance," Price added.

Price also sold the bill's plan to change Medicaid to a system of block grants to the states.

"Medicaid actually becomes much more flexible for states so that they can design a program that works for them as opposed to Washington telling the states what they want," Price said.

Price's appearance on a Sunday show wouldn't have been predicted a week ago, as the Senate leadership was hopeful they could have had a successful vote before the July 4 recess.

But Senate Majority Leader Mitch McConnell postponed the vote after a number of high-profile members of his caucus indicated they couldn't support the bill as it stood, or that they needed more time for debate.

Recent days have seen President Trump become more active in selling the Republican healthcare reform plans, despite the president's self-created Twitter controversies.

Price said the five senators who have misgivings about the bill have all said that ultimately, they want to be able to get behind a Republican-led reform plan.

"That's the nature of the legislative process and that's what we've been working through this week," Price said of the administration's conversations with Sens. Rand Paul of Kentucky, Ted Cruz of Texas, and others.