Those comments were contained in minutes from the Fed's December meeting, which were released Thursday afternoon. (Read More: End of Stimulus? What's Behind the Fed's Surprise Statement.)
"Why are we talking about dates?" Bullard asked in a "Power Lunch" interview. "If the economy performs well in 2013, the committee will be in a position to think about going on pause with its balance sheet policy. If it doesn't do very well then the balance sheet policy will continue into 2014. That's the beauty of doing it this way instead of doing it by a fixed date." (Read More: Why the Fed's Not Going Anywhere)
The Fed previously had tied its expectations for policy changes to a target date. But in December, the central bank made the unprecedented move of linking its bond buying program to unemployment, pledging to continue the stimulus until the U.S. jobless rate falls to 6.5 percent.
Bullard expects the employment rate to tick down in 2013, reaching about 7 percent by year-end. That improvement could be enough to allow the Fed to start considering ending its asset purchases, Bullard said.
Minutes from the December meeting indicated several members would like to stop the bond-buying program before 2014.
These members are increasingly concerned about the potential risks of the Fed's asset purchase on financial markets as the central bank's balance sheet has expanded to $2.9 trillion in the aftermath of the the financial crisis and recession of 2007-2009.
While not a voting member of the policy committee in 2012, Bullard is a voting member this year.
Resolving the country's fiscal problems could improve the outlook for the U.S. economy. Calling the debt ceiling "a dangerous thing to fight over," Bullard said, "If you could get rid of the medium-term and longer-run uncertainty about the U.S. fiscal outlook, I think it would be a tremendous help to the U.S. economy."