In an opinion article in the Financial Times, Roubini said that the deal did prevent the US economy from falling of the fiscal cliff, but added that "given the dysfunctional nature of the American political system, it won't be long before there is another crisis."
Analysts have warned that the deal was just a temporary solution, as it did not include the thorny issue of raising the debt ceiling, nor spending cuts.
A "big fight about entitlements," as well as "a series of little fights over tax reform" are ahead, with questions such as whether the US should introduce a value added tax, a flat tax, or a carbon tax, whether income taxes should be higher or lower and whether corporate tax loopholes should be closed to raise more revenue, Roubini wrote.
"It'll soon get messy," he added.
Roubini predicted that the fiscal adjustment probable this year, spread between the expiry of the payroll tax cut, the increase in taxes for the rich and some cuts to spending, would be around 1.4% of gross domestic product, which would translate into "a 1.2% of GDP drag on the economy during the year."
He pointed out that if the economy was "happily growing above trend", at about 3.5%, "that would not be such a big deal, as growth would still be above 2%."
But, Roubini added, "in the past few quarters growth already averaged about 2%. So the US could quite easily come perilously close to stall speed this year – or worse, if the eurozone crisis worsens."
Roubini, who is famous for his pessimistic predictions which have earned him the nickname "Dr. Doom" in the media, said that it would probably "take years" for the US to raise fiscal revenues to a level that would allow them to fund a reformed welfare state. Bond market "vigilantes" have "no appetite for destruction" now as inflation is low and the US still has the global reserve currency - meaning US Treasuries are safe-haven assets bought by China and other emerging economies, which also buy dollars to keep their currencies from appreciating.
"But eventually, the vigilantes will wake up," he predicted.