More Americans disapprove than approve of President Obama's "fiscal cliff" deal that eliminated the payroll tax holiday and raised taxes on incomes over $400,000, according to a new poll.

In the survey from The New York Times and CBS News, 47 percent say they disapprove of the president's handling of taxes, while 45 percent approve. That's a shift from the lead-up to the compromise deal, when the president enjoyed majority support for his tax plan. In December, 52 percent approved of Obama's handling of taxes.

The president also received poor marks on his handling of the federal budget deficit, with 54 percent of Americans — and a quarter of Democrats — disapproving of his handling of the nation's debt. By contrast, just 37 percent approve.

Obama was also unable to earn plurality approval among those asked about his handling of the economy. While 46 percent approve of the way he is dealing with economic matters, 49 percent disapprove.

The president's shortcomings on economic matters come despite an American public that is generally high on the president. A majority of those surveyed, 51 percent, approve of the way Obama is handling his job overall. That's similar to President George W. Bush's numbers heading into a second term, but far behind former Presidents Clinton (60 percent) and Reagan (62 percent) heading into their second terms.