And while there are currently tax credits in place to help offset costs, the current bill reduces those tax credits, he noted. "There's a double whammy here."

"Right now, health care is barely affordable for those people who are over age 50. Raising it any more is just what we call an 'age tax' and would just make it unaffordable for them," David Certner, legislative counsel and legislative policy director for government affairs at AARP, said in an interview with " Power Lunch ."

Under the new legislation, insurers would be allowed to charge older adults up to five times more than younger people. Under Obamacare, rates were capped at three times more.

A patient is monitored in an examination room inside the Clinical Decision Unit at Kaiser Permanente's Capitol Hill Medical Center in Washington, D.C.

Senate Republicans released their bill, called the "Better Care Reconciliation Act of 2017" last week. On Monday, they released changes to the legislation, including a six-month waiting period for people who have let their insurance coverage lapse for more than 63 days.

Among other things, the bill calls for younger people to pay less of a share of their income toward their individual health plans compared with what they pay now under Obamacare. Older adults would end up paying a larger share of their income.

Jeff Miron, director of economic studies at the Cato Institute and legislative policy director for government affairs at Harvard, believes it's the right policy to make the system work efficiently.

"Letting the insurance premiums reflect the riskiness of the people who are being insured across different ages or possibly other groups is entirely rational," he told "Power Lunch."

While he acknowledged the policy would be bad for those who are already elderly, he pointed out that over a long period it wouldn't necessarily harm anyone.

"When you're young you'll pay the relatively low rates. When your middle age you'll pay somewhat higher rates and when you are old you'll pay the very high rates. But on average that should be the same for everyone," Miron said.

"It is only current near elderly who are going get particularly penalized by this transitional effect," he added.

The bigger issue, said Certner, is what can be done to control the cost of health care.



"Everybody wins, no matter what the age is if we help hold down health-care costs in this country," he said. "The bills that have been put forward by both the House and the Senate do absolutely nothing to address the underlying issues of high health-care costs and high prescription drug costs."

— CNBC's Bertha Coombs, Dan Mangan and Reuters contributed to this report.