Treasury yields have confounded the market consensus for an increase this year, falling from 2.17 percent at the end of 2014.

And Scott Minerd, global chief investment officer for Guggenheim Investments, believes the trend will continue. "The big question is will the overflow of negative yields in Europe push us to levels on interest rates in the U.S. that we think would be completely [unsustainable]," he tells CNBC. "That's the risk."

In Germany, government bonds (bunds) with maturities of up to five years have negative yields.

"If 10-year bunds were to go to a negative yield, could we see 10-year U.S. Treasurys at 1 percent or lower?" Minerd asks. "I wouldn't rule it out." Ten-year bunds yielded 0.17 percent Thursday.

The dollar's strength will help attract investors to Treasurys, he notes. The euro fell to a 12-year low against the greenback last month.

The euro could fall to 80 to 85 cents this year, Minerd predicts. Given that scenario, "why wouldn't European investors continue piling into U.S. Treasurys?"

But things could change for the better in Europe.

The eurozone economy grew only 0.9 percent last year, and coming into this year many analysts were concerned about the possibility of another recession.

However, "the latest economic data from the eurozone suggest that recovery may be at hand," economist Nouriel Roubini of New York University writes in an article for Project Syndicate.

Aggressive easing by the European Central Bank (ECB) has helped spark the rebound, he says. The ECB is buying 60 billion euros ($65 billion) of bonds a month to jumpstart the economy. And the euro's drop has boosted exports.

"But a more robust and sustained recovery still faces many challenges. For starters, political risks could derail progress," Roubini writes. "Slow job creation and income growth may continue to fuel the populist backlash against austerity and reform," he says.

So what should Europe do to extend the recovery?

"Germany needs to adopt policies — fiscal stimulus, higher spending on infrastructure and public investment and more rapid wage growth — that would boost domestic spending and reduce the country's external surplus," Roubini argues.

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