Taxes for most Americans will still go up this year despite declarations from President Obama and others touting Tuesday night's fiscal crisis deal as a victory for middle-class workers.

At the same time, tax relief that was included in the package comes at a cost -- contributing, along with new spending, nearly $4 trillion to the deficit over the next 10 years, adding to the nation's more than $16 trillion debt.

But there will be federal tax hikes in 2013. That's because the legislation pushed through the Senate and House on Jan. 1 does nothing to prevent a temporary cut in the Social Security payroll tax from expiring. That means, under the agreement brokered by the White House and Senate Republicans, 77 percent of American households will be forced to fork over higher federal taxes in 2013.

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 families, the increase will end there. But for top earners, taxes will get considerably higher this year.

The package passed by both chambers extends most the Bush-era tax rates for individuals making less than $400,000 and married couples making less than $450,000 -- but lets them lapse for income above those thresholds.

The new tax package would increase the top income tax rate from 35 percent to 39.6 percent. Investment taxes would also increase for people who fall in the new top tax bracket, from a rate of 15 percent to 20 percent.

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," Roberton Williams, a senior fellow at the Tax Policy Center.

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.

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.

The deal passed Tuesday night only tees up a new round of congressional battles in a matter of weeks over the debt ceiling and automatic spending cuts that would largely hit the Pentagon -- the latter provision was delayed by two months as part of the deal. Democrats are likely to continue pushing for tax hikes as part of those debates, while Republicans are demanding spending cuts and entitlement reform.

The Associated Press contributed to this report.