Sen. Ted Cruz on Saturday pushed his amendment to the Senate healthcare bill, saying his Consumer Freedom Amendment would bridge the divide in the Republican Party.

"I believe it's the key for bringing everybody together," the Texas Republican said. "If premiums go down, that's a big win, for conservatives, moderates, for everyone in the party, because it's a win for our constituents," the Texas Republican said on Fox Business.

Senate Majority Leader Mitch McConnell is struggling to gather 50 votes for the Better Care Reconciliation Act, with conservatives opposed because it doesn't repeal enough of Obamacare and moderates concerned about its cuts to Medicaid and reductions in coverage.

The Congressional Budget Office has not scored the Cruz amendment, which would let insurers sell plans that don't comply with Obamacare's mandates as long as they sell one that does. Cruz said the nonpartisan office would not have time, with the Senate expected to vote on a healthcare bill next week, but pointed out that the Department of Health and Human Services did its own assessment.

"They projected with the Consumer Freedom Amendment, 2.2 million more people will get health insurance … would lower consumer premiums by $7,000 a year," Cruz told Fox Business.

Healthcare experts have criticized the HHS analysis as flawed, saying the methodology is wrong and it leaves out key data.

Cruz said part of his amendment would allow people to use health savings accounts to pay for premiums. Pointing out that health saving accounts are pre-taxed, meaning it would be "an immediate cut for millions of people."