One such critic, Jeffrey Lacker, president of the Federal Reserve Bank of Richmond, has cast a lone dissenting vote at all seven Fed policy meetings this year. Lacker has said he thinks the job market is being slowed by factors beyond the Fed's control. And he says further bond purchases risk worsening future inflation.
Others, like John Williams, president of the San Francisco Fed, have said they think the Fed's bond purchases must continue because the job market and other components of the economy are improving only gradually.
The Fed is also expected this week to resume discussions on how to signal future policy moves to the public more clearly. Since August 2011, the Fed has identified a target date to try to reassure markets that it doesn't plan to raise short-term rates soon.
Some Fed officials, however, oppose using a target period to signal the earliest when it might start raising rates. They've been urging that future interest-rate moves be linked to how the economy is faring as measured by unemployment and inflation.
Chicago Fed President Charles Evans, a proponent of this change, would set the unemployment target at 6.5 percent and the inflation target at 2.5 percent. If those targets were adopted, the Fed would say it didn't plan to raise rates until unemployment drops below 6.5 percent — as long as the Fed's inflation gauge is no more than 2.5 percent. The Fed's inflation measure over the past 12 months has risen just 1.7 percent, signaling that inflation pressures are well-contained.
Many private economists expect no change in the Fed's communications strategy this week. They think officials are far from a consensus on how to adopt numerical targets for any interest-rate move. But a change could come next year.
By contrast, there's widespread expectation that the Fed will announce a program to replace Operation Twist. If it didn't, the Fed's support for the economy would be reduced at a time when growth is weak and unemployment still high .
"They can't have the current level of bond buying come to an end with all the uncertainty of the fiscal cliff just around the corner," said Greg McBride, senior financial analyst at Bankrate.com.
The Fed's meeting coincides with negotiations between Congress and President Barack Obama over a budget deal to avert the fiscal cliff. The talks are focused on Obama's push to raise tax rates for the top 2 percent of income earners. Most Republicans are resisting such a move.
Brian Bethune, an economics professor at Gordon College, says he thinks Fed officials this week might discuss what further action they could take if Congress and the administration fail to reach a deal before January and the tax increases and spending cuts take effect.
"We are in unusual times, and that may require an unusual amount of Fed policy actions," Bethune said.