House Republicans boast that their health care bill would reduce average premiums, but that's because the insurance policies will generally cover less.

That might be fine for those who never see the doctor, but it would mean those who actually use the coverage will pay more to get treatment. Those additional out-of-pocket costs could total thousands of dollars more, in some cases, according to a Congressional Budget Office analysis of the bill.

Much of the debate surrounding Obamacare has focused on how much people pay each month for coverage. Republicans have repeatedly touted their bill as lowering premiums, but they've said less about how it would affect what consumers have to shell out for care.

Obamacare put in place an array of protections that pushed up premiums, but shielded Americans from big health care bills. It required insurers to sell comprehensive policies that cover 10 essential health benefits, including hospitalization, prescription drugs, mental health and maternity care. It mandated carriers shoulder a certain share of the costs of covered benefits.

Also, the law capped how much consumers have to pay out-of-pocket each year for the essential health benefits -- $7,150 in 2017 -- and it prevented insurers from settling annual or lifetime limits on these benefits.

Related: 23 million fewer Americans insured under House GOP bill, says CBO

The GOP's American Health Care Act would weaken many of those provisions. Most notably, it would allow states to waive the federal essential health benefits mandate and set their own rules on what carriers must cover.

(On top of this, the legislation would also allow states to waive the requirement that insurers charge healthy and sick consumers the same premiums. Instead, carriers would be allowed to set rates based on enrollees' medical history -- meaning older policyholders and those with pre-existing conditions would face higher premiums, while the healthy would enjoy lower rates, the CBO found.)

About half of Americans live in states that would opt out of the essential health benefits mandate, estimated the CBO report, which came out Wednesday.

Not all of them would feel a change since not everyone uses a lot of health services every year, said Dave Dillon, fellow with the Society of Actuaries. But those that do could find themselves paying more for care that's no longer mandated.

The CBO report put it more bluntly: "As a result of the narrower scope of benefits included in many plans, however, enrollees who would use services that were not covered by the available plans would face substantial increases in their out-of-pocket costs under the act ... Some people would have increases of thousands of dollars in a year."

What would likely be on the chopping block? Maternity care, mental health, substance abuse, rehab services and pediatric dental care, the analysis found. Prescription drug coverage would likely be limited as well. Prior to Obamacare these services typically were not covered.

Related: Who gets hurt and who gets helped if Obamacare is repealed

Even if insurers decide to offer additional services, they'd be free to place annual or lifetime limits on that coverage, and policyholders would not be protected by an annual cap on out-of-pocket costs. That's because these Obamacare protections only apply to essential health benefits.

In some states, policies would cover so little that those enrolled in them would be considered uninsured under the CBO's definition.

Republicans have often knocked Obamacare for having such high deductibles that enrollees don't really have coverage even though they have an insurance card. The CBO notes that under the GOP bill, many older Americans and those who use services that were no longer covered would find themselves in the same boat.