Obamacare has been credited with expanding coverage to 20 million Americans in past several years. The House bill would remove the requirement that most people have some form of insurance or pay a fine, and reduce the amount of money the federal government spends on subsidies for insurance plans and Medicaid.

The CMS actuary estimated that in the individual insurance plan market, "average gross premiums are estimated to be roughly 13 percent lower in 2026 under the AHCA than under current law."

But, he added, average net premiums, or the monthly cost of the insurance after government subsidies to customers are factored in, "are roughly 5 percent higher than under current law."

And the average amount of money customers would be liable to personally pay out of pocket for health services or prescriptions they receive are projected to be about 61 percent higher under the AHCA than if Obamacare remained in place.

CBO's estimate of the AHCA's effect on premiums did not factor in subsidies. But it was more complicated than the actuary's estimate because it calculated the effects of whether a state did or did not request waivers from Obamacare rules requiring insurers to not charge sicker customers higher premiums, and from rules requiring insurers to offer customers a certain minimum set of benefits.

In some states that did not request waivers, CBO said, premiums would be about 4 percent lower than they would be if Obamacare stayed the law of the land. In other states that made moderate changes to regulations, average premiums would be about 20 percent lower than current laws.

And premiums would be even lower in other states that were aggressive in obtaining waivers, but "less healthy people would face extremely high premiums," CBO said.

Elsewhere in his new report, CMS's actuary estimated there would be an increase of direct out-of-pocket health spending by households of almost $221 billion under the AHCA. That increase in spending will be "almost entirely offset by lower spending because of declines in employer-sponsored coverage, a reduction in the additional Medicare tax for high-income earners, and the effect of the elimination of the health insurance tax on premiums" under the bill.

Nicole Gill, executive director of the advocacy group Tax March, said, "The Trump Administration's own Centers for Medicare and Medicaid Services released a report today proving that the American Health Care Act would be a disaster for American families as it increases their out-of-pocket health care costs by an astounding $221 billion over the next ten years."

"That is a stunning jump in cost-sharing that will be a heavy burden for American families, all to pay for tax cuts for the rich," Gill said. "This report proves one thing: This bill literally takes money out of the pockets of working families to pad the wallets of millionaires and billionaires."

Also Tuesday, Trump traveled to Milwaukee, Wisconsin, where he blasted Obamacare and Democrats whom he accused of obstructing his efforts and those of congressional Republicans to fix the health insurance system.

Trump called Obamacare "a catastrophe," and said "millions of Americans, and I mean millions, continue to suffer" from the program.

The president said many people have been saddled with ever-increasing insurance premiums, and have had to deal with insurers abandoning markets.

But, he added, "the Senate is getting ready to do something."

Despite that promise, and despite GOP control of both chambers of Congress, both Trump and Congressional Republicans have found it is taking longer than they had hoped to achieve that goal.

The House bill passed that chamber by a margin of just a single vote in May.

Since then, a group of GOP senators have been meeting, without any Democratic colleagues in attendance, to discuss the framework of their own Obamacare replacement bill.