The White House believes enrollment in Obamacare plans will not be markedly different as a result of repealing the penalties Americans face if they don't buy insurance, despite several projections showing millions more will become uninsured.

"With the repeal of the individual mandate you will actually not see a huge sea change in signing up," a senior White House official told the Washington Examiner.

The official noted that many people are already uninsured under Obamacare, and made that choice even though it led to a penalty. Under the tax bill passed by Congress Wednesday, people who are uninsured will no longer pay a fine.

The White House comments mirror those of many Republicans who say that the mandate did not propel people to buy health insurance who would otherwise not have done so.

But they clash with studies by the Congressional Budget Office, which projected that 13 million more people would be uninsured if the mandate penalties were repealed. The agency is re-visiting its analysis, and a Standard & Poor analysis projected the number of people who do not have health insurance will increase by 5 million at most.

The penalty will go off the books beginning in 2019. Until then, penalties are $695 per adult, or 2.5 percent of income, whichever is higher.

The requirement for insurance companies to cover enrollees with pre-existing illnesses without charging them more will remain in effect. But insurers have warned that to meet this requirement, they will have to raise the costs of premiums or quit the exchanges altogether. These actions could have an impact on enrollment, actuaries, and insurers have warned.

While the White House official said Obamacare signups won't change much, President Trump celebrated the passage of the tax bill with lawmakers at the White House on Wednesday and said the bill is a grave blow to the law.

"I hate to say this but we essentially repealed Obamacare ... the individual mandate which was terrible," Trump said at the White House event.

Andrew Bremberg, director of the Domestic Policy Council for President Trump, called the repeal of the mandate penalties an "important legislative accomplishment."

"I think this makes clear that the Democrats are finally admitting to the American people that they want to tax Americans, even those who cannot afford health insurance that has been made more expensive by Obamacare," he said in a phone interview.

Bremberg added that the tax "disproportionately hits lower- and middle-income families," noting that nearly 80 percent of people who paid the penalty made less than $50,000 a year, a figure that comes from 2015 Internal Revenue Service data.

Under Obamacare, people who make more than $48,240 a year for an individual or $94,400 for a family of four and are not eligible for subsidies because Obamacare cuts off assistance at 400 percent of the federal poverty level. Those who make below that receive subsidies that bring their share of premium costs closer to $75 to $100. Some customers will be heading into 2018 paying no premium for their coverage.

The senior White House official said the Trump administration supports other changes to the healthcare system and said a bill known as Graham-Cassidy that would allow states to create their own healthcare systems was one option, but others could be considered.

"We are open to all sorts of alternatives on how to deliver much better options than Obamacare," the official said.