That growth could fall so low in a quarter in which the Federal Reserve was engaging in a new round of quantitative easing, buying $85 billion of bonds each month, might cast doubt on the effectiveness of the program. That would be bad news for stocks, which rose for the first four months of the year on the idea that QE could prop up a weak economy. (And have recently fallen after the Fed began to explain when it would pare back the program.)
"'QE on' was a misguided speculative bubble in any case, as QE is, at best, a placebo, and in fact somewhat of a tax as it removes a bit of interest income," bond investor Warren Mosler said.
Mosler is a long-term critic of QE. He believes that because the interest paid on bonds the Fed buys under the program gets paid to the Fed instead of private bond holders, it acts as a tax on the private sector. The economic benefits are illusory, according to Mosler.
(Read More: Should the Fed Run Payroll Taxes?)
On the other hand, sluggishness in the economy could mean that expectations about the Fed tapering QE and raising rates get pushed back. Bernanke has stressed that decisions about policy changes would be dependent on economic data.
Wednesday's news about the first quarter, while backward looking, certainly casts doubt on whether the economy is strong enough to justify lower levels of bond purchases.
Not everyone buys that way of thinking, however. Some doubt that Wednesday's news will have any effect on the Fed's plan to reduce the bond-buying program.
"The Fed will presumably continue to maintain its primary focus on labor market data, so while this revision obviously will impact their thoughts at the margin, I highly doubt that it will be a game changer, especially since I am skeptical that policymakers are as data-dependent as they want to believe," Stephen Stanley of Pierpont Securities wrote in a note Wednesday morning.
—By CNBC's John Carney. Follow him on Twitter