"I think we'll test 1.30 before the end of the year. The big question is are we going to stall there, or have a big clean break?" said Jens Nordvig, Nomura's global head of G-10 foreign exchange strategy.
European leaders agreed to a tighter plan of fiscal integration, including central authority over budgets and deficits.
"Now, it looks like it wasn't enough for the market," said Mary Nicola, currency strategist with BNP Paribas. "Especially the prospects of anything coming out of the ECB . It looks dimmer and dimmer."
Strategists said the market's big disappointment is that the European Central Bank is showing no signs of stepping up its bond purchases, despite the fact that ECB President Mario Draghi signaled the ECB would not expand its purchases after its rate meeting last Thursday. He had led the market to believe the week earlier that the ECB might play a bigger role if the EU leaders took action to create a stronger fiscal union.
"Everyone was hoping if there were some kind of stronger agreement...we'd see some step up in [bond] buying, and there wasn't" any, Nicola said. She said another dark cloud over the euro is the comments from rating agencies that they are reviewing the European sovereigns.
Fitch Monday said it did not see a comprehensive solution to the sovereign crisis , and it expects it to continue at varying levels of intensity beyond 2012. It also forecast a significant economic downturn across the euro zone in the near term.
The ECB is "the only truly credible firewall against liquidity and even solvency crisis in Europe," Fitch said. Moody's also commented on the summit's failure to find decisive policy measures to end the crisis and it warned it would review all the EU countries' ratings.
As risk assets sold off, spreads on European sovereigns once again widened, with the Italian 10-year again heading toward the 7 percent level.
"If we have a situation where we have the Italian bond yields heading toward 7 percent, it is going to be difficult for global markets to ignore them," Nordvig said.
Brian Dolan, chief strategist at Forex.com, said the euro hit a technical zone at 132.50 and it eventually could drop to 1.28. Nicola expects the euro to trade in its current range until the end of the year, then she too sees a move to 1.28 in the first quarter.