Other economists have predicted that Greece will default, with one saying that this may happen as early as in August.
Spain "is worse in some ways," according to Roubini, because unemployment there has reached 20 percent, not 10 percent like in Greece, the country's housing bubble has burst and it is one of the top four economies in the euro zone. A Spanish breakdown would be "a disaster," he said.
Yields on Spanish T-bills jumped in an auction Tuesday, raising doubts over the country's credit rating as they were much higher than those on T-bills of triple-A rated peers.
"There is no calm" in the markets, Roubini said.
"Markets are now realizing that this is going to be a period of slow economic growth. I'm not doom and gloom, I'm talking about slow economic growth over the next 3 years," Roubini, who has been nicknamed "Dr. Doom," said.
Economic growth below 2 percent in the US would make for a negative outlook, and this scenario is very likely, he said.
The US economy needs to create 150,000 jobs per month to stabilize the labor market, and it is creating fewer, according to Roubini, who sees unemployment staying close to 10 percent.
The US must take advantage of the fact that euro weakness is sending money into Treasurys and think about economic growth in the short run, while having a credible fiscal plan in the medium term, Roubini added.