According to David Woo, head of global rates and currencies strategy at Bank of America Merrill Lynch, "with the euro area running a current account surplus, a precondition for a lower euro is increased purchases of foreign securities by European investors. So far this year, European investors have been happy to stay close to home—European fixed income assets have done very well this year, especially on a volatility-adjusted basis."
At the same time, "the consensus remains that a significant selloff in U.S. Treasurys has yet to come."
"By doing whatever it takes to support the euro zone, the ECB takes the tail risk out of the equation," said Rosenberg, referring to a potential euro zone collapse and breakup.
"That strengthens the euro. And that impact offsets the interest rate policies that may lead to a weaker euro. … In this line of thinking, currencies are not an asset class by themselves. Rather they are a means to owning an asset class, whether it be stocks, bonds, real assets, etc."
Read MoreMerkel talks tough, but can Europe back it up?
The next path for the euro could be determined by whether the voracious demand holds up for European stocks and bonds.
And watch whether U.S. Treasury yields stay historically low or start to creep higher on rising inflation expectations, higher interest rates or a better economy.
There's also the third factor to keep in mind—big money loves the euro.
"Reserve diversification into euros is strong. For each U.S. dollar of diversification our analysis of 87 reserve managers shows 67 percent bought euros versus the dollar," said Sebastien Galy, senior currency strategist at Societe Generale.
In Societe Generale's survey published this month, 11 percent of those dollars went to buying yen, 5.4 percent Australia's dollar and smaller amounts of British pounds and Chinese yuan.
Beyond the daily swings in European stocks and bonds, and shifting expectations for interest rates, inflation and economic growth, there is a fundamental bid and growing trust in the euro.
—By CNBC's Sara Eisen