But an accelerating U.S. economy with the euro zone wallowing in a deflationary, sluggish growth environment has fueled talk about an even lower level for the euro. That talk comes against a backdrop of superlow interest rates in Europe—with German bunds at negative yields up through the five-year.  U.S. Treasurys, at the long end of the curve, have seen intense buying since the start of the year, which has driven U.S. yields lower. The 10-year yield was higher Wednesday but still below 2 percent.  "I'm just thinking a lot of that is already in the market. Based on current interest rate differentials, it suggests euro-dollar should be trading at 1.25 but we're at 1.18." Sinche said $1.25 should be the top of the euro's range this year.  But Chandler is more negative on the euro. "Maybe the Swiss National Bank is the only real buyer of the euro," he said. Chandler said Switzerland's central bank intervened to defend its cap against the euro last month. The SNB increased its reserves by 7 percent in November.  Read MoreEurozone economy ended 2014 on low note  "I think even in the best of times, Europe's likely to grow at 2 percent. I think the decline in the euro, the decline in interest rates, the decline in oil is going to help put a floor under the European economy," he said.  Chandler said the U.S. economy, meanwhile, will help support a rising dollar. "The euro goes down. The U.S. gets better. Just as the euro had an overshoot to the upside, it gets to overshoot to the downside ... I think a lot depends on what happens in the U.S."
Unthinkable even a few weeks ago, but now pros are saying the weakening currency may fall so low it could trade at parity with the dollar—or even lower.