WASHINGTON — While the tax package that Congress passed New Year’s Day will protect 99 percent of Americans from an income tax increase, most of them will still end up paying more federal taxes in 2013.

That’s because the legislation did nothing to prevent a temporary reduction in the Social Security payroll tax from expiring. In 2012, that 2-percentage-point cut in the payroll tax was worth about $1,000 to a worker making $50,000 a year.

The Tax Policy Center, a nonpartisan Washington research group, estimates that 77 percent of American households will face higher federal taxes in 2013 under the agreement negotiated between President Barack Obama and Senate Republicans. High-income families will feel the biggest tax increases, but many middle- and low-income families will pay higher taxes too.

Households making between $40,000 and $50,000 will face an average tax increase of $579 in 2013, according to the Tax Policy Center’s analysis. Households making between $50,000 and $75,000 will face an average tax increase of $822.

“For most people, it’s just the payroll tax,” said Roberton Williams, a senior fellow at the Tax Policy Center.

The tax increases could be a lot higher. A huge package of tax cuts first enacted under President George W. Bush was scheduled to expire Tuesday as part of the “fiscal cliff.” The Bush-era tax cuts lowered taxes for families at every income level, reduced investment taxes and the estate tax, and enhanced a number of tax credits, including a $1,000-per-child credit.

The package passed Tuesday by the Senate and House extends most the Bush-era tax cuts for individuals making less than $400,000 and married couples making less than $450,000.

Obama said the deal “protects 98 percent of Americans and 97 percent of small business owners from a middle-class tax hike. While neither Democrats nor Republicans got everything they wanted, this agreement is the right thing to do for our country.”

The income threshold covers more than 99 percent of all households, exceeding Obama’s claim, according to the Tax Policy Center. However, the increase in payroll taxes will hit nearly every wage earner.

Social Security is financed by a 12.4 percent tax on wages up to $113,700, with employers paying half and workers paying the other half. Obama and Congress reduced the share paid by workers from 6.2 percent to 4.2 percent for 2011 and 2012, saving a typical family about $1,000 a year.

Obama pushed hard to enact the payroll tax cut for 2011 and to extend it through 2012. But it was never fully embraced by either party, and this time around, there was general agreement to let it expire.

The new tax package would increase the income tax rate from 35 percent to 39.6 percent on income above $400,000 for individuals and $450,000 for married couples. Investment taxes would increase for people who fall in the new top tax bracket.

High-income families will also pay higher taxes this year as part of Obama’s 2010 health care law. As part of that law, a new 3.8 percent tax is being imposed on investment income for individuals making more than $200,000 a year and couples making more than $250,000.

Together, the new tax package and Obama’s health care law will produce significant tax increases for many high-income families.

For 2013, households making between $500,000 and $1 million would get an average tax increase of $14,812, according to the Tax Policy Center analysis. Households making more than $1 million would get an average tax increase of $170,341.

“If you’re rich, you’re almost certain to get a big tax increase,” Williams said.