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.

Perhaps more troubling, however, is the notion that it might not take a default for yields to rise in the long term. The standoff over the debt ceiling could have done enough damage already, Tucker said.

"Even if we get through this period, and even if we don't see a downgrade or the Treasury makes it through, what does this do to the long-term role of the Treasury as the world's reserve currency and reserve investment?" he asked.

"I think events like we saw in 2011 are weakening that role and creating the possibility that some other major sovereign issuer could step in as being that global, flight-to-safety instrument," Tucker said. "And I think that creates a real threat to the Treasury and its ability to finance itself long term."

(Read more: With bonds in limbo, here's how to cash in: Pro)

That said, he doesn't believe that yields will end the year much higher than they are today.

"If you look at the factors that are still keeping yields low, the Fed is still in play," Tucker said. "It doesn't look like tapering's going to occur any time this year. So it's difficult to see a significantly higher rate."

"But obviously," he added, "if we do get some extreme event coming from the talks in Washington, then you could actually see a rally" in Treasury yields.

—By CNBC's Alex Rosenberg. Follow him on Twitter: @CNBCAlex.

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