The government left the door wide open for millions of Americans to be excused from the Affordable Care Act’s requirement that most people must carry health insurance or pay a fine, but so far relatively few have asked for such a pardon.

About 77,000 families and individuals have requested exemptions from the health-care law’s so-called individual mandate, according to internal government documents obtained by The Washington Post. As of April 20, officials had approved tens of thousands of exemption requests and rejected none.

The rest are on hold or in the process of being vetted. Even so, the numbers are relatively small compared with the 8 million who have enrolled in private coverage on the state and federal marketplaces — a sign that people taking action as a result of the health-care law are by and large choosing to comply with the mandate, long the most unpopular aspect of the program.

Republicans have been sharply critical not only of the mandate but also of the many ways a person can skirt it. Various categories of people, including those belonging to certain religious groups, Native Americans and illegal immigrants, may request an exemption. There are also 14 “hardship” categories, some of them rather broad.

Republicans have reserved particular criticism for a vaguely worded, catchall category added in December — an exemption available to anyone who “experienced another hardship in obtaining health insurance.”

“There’s a real question as to whether the White House just abandoned the individual mandate, the heart of Obamacare itself,” House Speaker John A. Boehner (R-Ohio) told reporters last month.

But the documents show that there has not been a wave of people seeking this exemption. Serco, the company processing the exemptions for every state except Connecticut, reported receiving 2,700 such applications as of April 20. Those applications are being set aside until federal officials provide guidance on how they are to be judged, the documents show.

Officials with the Centers for Medicare and Medicaid Services, the federal health agency overseeing much of the implementation of the health-care law, said Friday that the agency is working with those individuals to see if their circumstances fit into a different exemption category.

Serco also has not yet processed more than 20,000 applications from people who say they cannot afford insurance. CMS officials said they are in the final stages of testing a tool that will allow them to calculate eligibility for an exemption based on income.

Of the 76,859 exemption applications received by Serco as of April 20, the company had processed about 26,000, representing as many as 43,699 individuals.

The numbers provide only an initial snapshot, because people can apply for exemptions year-round. Some will get automatic exemptions — for example, if they make too little money to be required to file tax returns. Others will be able to get one when they file their 2014 taxes next year.

The Obama administration has projected that 12 million people will seek exemptions to the insurance mandate in 2016.

Graphic The ACA's 21 deadline extensions A look back at every Affordable Care Act deadline that was extended by the Obama administration.

The vast majority of exemption applications submitted so far — more than 32,000 — came from members of federally recognized American Indian or Alaska Native tribes. Native Americans were excluded from the mandate because the federal government is already responsible for their health care through the Indian Health Service.

Many Native Americans have been applying for exemptions simply because they can, but they later enroll in coverage when they realize that private insurance offers better benefits, said Jerilyn Church, chief executive of the Great Plains Tribal Chairmen’s Health Board, which is helping members of North Dakota and South Dakota Indian tribes enroll in health insurance.

“A tribal member can apply for the exemption, but it doesn’t mean that they can’t apply for [insurance on] the marketplace,” Church said, adding that many are filling out exemption forms “just to cover their bases.”

The second largest group is those receiving religious exemptions, with more than 11,000 exemptions approved as of April 20. There have been organized efforts to file exemptions in Amish, Mennonite and Hutterite communities — religious groups that oppose insurance and already are exempt from Social Security and Medicare.

One category of people expected to make up a large proportion of those with exemptions are those who would have been able to join Medicaid if their states took up the health law’s optional expansion of the program.

That could cover about 7.6 million Americans, according to the nonpartisan Kaiser Family Foundation. However, the majority of those people make so little money that they are not required to file taxes and therefore do not have to fill out any form to be pardoned from the mandate.

Others in that group will have to fill out a form — something few are eager to do after learning that they do not qualify for Medicaid, said Jason Stevenson, spokesman for the Utah Health Policy Project, a group that receives federal funding to help people sign up for insurance.

“Most people are so upset that the last thing they want to do is fill out another government application,” he said.

As of April 20, Serco had received about 11,400 general hardship exemption applications, of which this Medicaid-ineligible population is a subset.