Sen. Bill Cassidy, R-La., on Tuesday said that a proposal to would roll back Obamacare's regulations in states was a "violation of President Trump's pledge" to voters.

In discussions to repeal and replace Obamacare, Republicans in the Senate have raised the possibility of more aggressively rolling back Obamacare's insurance regulations so that states have to actively opt in to keep them. This proposal has rattled centrists who believe that a House bill to repeal Obamacare, called the American Health Care Act, went too far in changing the healthcare law's regulatory structure.

It is also a different proposal than the House bill itself, which keeps Obamacare regulations as the default nationally and requires states to seek waivers to get out of regulations on what medical provisions a plan must provide and how it prices people with pre-existing illnesses.

Cassidy, who has drafted his own bill with fellow centrist Republican Sen. Susan Collins of Maine, has spoken out about his problems with other Republican proposals and said that he believes a bill to repeal and replace Obamacare must follow Trump's promises to not take away coverage from people who are insured, to lower premiums and to cover people with pre-existing conditions.

"That would clearly violate President Trumps' pledge," Cassidy said in a meeting with reporters, answering a question about the proposal. "So if you decide that President Trump's pledge, his contract with the voter, is not important, then do what you want. But if you think Trump's pledge, to those Trump voters [matters] … then you have to worry about it."

He also took issue with the way the proposals have been crafted to place only sick enrollees separate from the rest of the risk pool.

"There seems to be a problem with our understanding of insurance," he said. "I'm afraid that some are looking at insurance as, 'We want to segregate those who are sick from those who are well.' That's not actually how insurance works."

"The way to address it is not to put sick people over here. They are still going to cost you an arm and a leg … rather it is to create your pool so large, just like the ocean with a cup of water poured in, so that one person's expensive illness is spread out among the many and does not cause premiums to budge."

Cassidy used the opportunity to speak to reporters about his bill, which provides for states to auto-enroll people who are uninsured into a high-deductible plan that is paid for by a tax credit, and that also would allow people to opt out if they choose.