"The Republicans are going to get this done. They have to get this done. There's just no option," Cantor said on "Squawk Box." He said health care is "the gateway to getting tax reform done and the rest."
The Republican former Virginia congressman also criticized the Congressional Budget Office's analysis of the GOP's Obamacare replacement, the American Health Care Act.
The CBO was not comparing apples to apples when estimating uninsured predictions. "The Obamacare replacement doesn't have in it a forced mechanism to make people buy insurance. That in and of itself is going to result in less people being covered."
The CBO said Monday a total of 24 million more Americans would be uninsured under the GOP plan than they would be under Obamacare by 2026.
The Trump-backed American Health Care Act would reduce federal deficits by $337 billion over the next decade, the CBO projected. But the CBO also said while premiums would likely be significantly lower, the Republican proposal would "substantially" raise premiums for older people.
While the House Republican health-care bill does not require people to buy health insurance or pay a tax penalty, it does allow insurance companies to apply a surcharge on people who drop coverage and then sign back up again.
"We are about freedom in America. And you're going to have a choice" on whether to buy health-care coverage," said Cantor, currently vice chairman and managing director at investment bank Moelis & Co. Cantor left congress after losing his 2014 Republican primary race to a tea party-affiliated economics professor.