It the U.S. goes into default because Congress fails to raise the debt ceiling, investors won't rush into bonds like they did in 2011, said Matt Tucker, BlackRock's head of iShares fixed-income strategy. Instead, Treasurys could sell off.

Many have compared this situation to the one in 2011, when Standard & Poor's downgraded U.S. debt because of "political brinksmanship." That tanked stocks, which sent people into Treasurys as a safe haven. So, investors paradoxically ended up buying more of the very asset class that S&P had downgraded.

But on Tuesday's "Futures Now," Tucker said that if the government is prevented from paying bills or spending money, the story could be very different.

(Read more: Reluctantly, market faces a real default threat)

"The difference here is that in 2011, we had a lot of concern about what was happening in Washington. This triggered a flight to safety, and Treasurys rallied," Tucker said. But, he added, "if we actually saw a default, whether it was a technical or otherwise default by the Treasury, that could be a very different reaction. You actually could see a more mixed response from Treasurys, even a selloff."

In fact, Tucker is already seeing holders of very short-term Treasurys demanding more yield to compensate them for the risk.

He noted that the Treasury bill maturing Oct. 31 is yielding more than the those maturing in January, which is quite unusual.

"The fact that the October T-bill is trading so high is a reflection of the uncertainty people have about the government making its payments," he said.