WASHINGTON – Nearly 4 million Americans — the vast majority of them middle class — will have to pay a penalty if they don’t get insurance when President Obama’s health care overhaul law kicks in, according to congressional estimates released Thursday.

The penalties will average a little more than $1,000 apiece in 2016, the Congressional Budget Office said in a report.

Most of the people paying the fine will be middle class as Obama’s comprehensive law is phased in over the next few years. In his 2008 campaign for the White House, Obama pledged not to raise taxes on individuals making less than $200,000 a year and couples making less than $250,000.

Republicans have criticized the requirement that Americans get coverage, even though the idea was originally proposed by the GOP in the 1990s and is part of the Massachusetts health care plan signed into law in 2006 by then Gov. Mitt Romney, a Republican. Attorneys general in more than a dozen states are working to challenge it in federal court as unconstitutional.

“The individual mandate tax will fall hardest on Americans who can least afford to pay it, many of whom were promised subsidies by the Democrats and who the president has promised would not pay higher taxes,” said Rep. Dave Camp of Michigan, the top Republican on the tax-writing House Ways and Means Committee.

About 3 million of those required to pay fines in 2016 will have incomes below $59,000 for individuals and $120,000 for families of four, according to the CBO projections. The other 900,000 people who must pay the fine will have higher incomes.

Sen. Chuck Grassley of Iowa, the top Republican on the Senate Finance Committee, said while Obama and congressional Democrats celebrate the benefits of the law, they have an obligation to acknowledge the flip side.

“There’s a price for not participating, and people will pay it,” Grassley said.

Democrats argue that the requirement and the penalties are a necessary part of a massive overhaul designed to expand coverage to millions who now lack it.

They point out that getting more Americans, especially young and healthy people, in the insurance pool will reduce costs for others and could lower premiums.

“The new law will make health insurance affordable for everyone and CBO’s analysis confirms that the vast majority of uninsured Americans will find health care affordable and choose to participate,” said White House spokesman Nick Papas.

Americans who don’t get qualified health insurance will be required to pay penalties starting in 2014, unless they are exempt because of low income, religious beliefs, or because they are members of American Indian tribes. The penalties will be fully phased in by 2016.

About 21 million nonelderly residents will be uninsured in 2016, according to projections by the CBO and the Joint Committee on Taxation. Most of those people will be exempt from the penalties.

Under the new law, the penalties will be phased in starting in 2014. 2016, those who must get insurance but don’t will be fined $695 or 2.5 percent of household income, whichever is greater.