The Federal Reserve should not go from "wild turkey" monetary policy to "cold turkey" overnight, Dallas Fed President Richard Fisher told CNBC on Monday, saying that when to dial back is the key because stopping would be "too violent for the marketplace."
He said the asset buying has helped boost the stock market, "but has it worked in the economy? ... We don't know."
"We're going to be at a point soon where ... [in] a couple of months, we could buying 100 percent of the gross issuance of mortgage-backed securities volume," he predicted. "We're going to be at a point where we're buying a significant portion—as these deficits come down slightly over the short term—of Treasury issuance."
Fisher, who's a non-voting member of the Federal Open Market Committee (FOMC) this year, said he's not alone among his peers in his thinking about scaling back asset purchases.
Last week's comments by the San Francisco Fed President John Williams and Philadelphia Fed President Charles Plosser suggested they were both were open to reducing asset purchases in the near-future.
(Read More: Start Tapering Asset Buys in June: Fed's Plosser)
Wall Street is paying close attention to these statements as investors and traders try to figure out when the Fed buying may slow down.
Last week, hedge fund manager David Tepper called for what could be termed the "Tepper Taper" in a "Squawk Box" interview. The Appaloosa Management founder told CNBC that the Fed needs to start tapering its asset purchases to keep stocks from going into "hyperdrive." He thinks a natural path will develop for the Fed to exit its accommodative stance.
(Read More: It's a 'My CousinVinny' Market, Bullish Tepper Says)
Policymakers have not seen the robust job creation that they'd like to see, the Fed's Fisher explained, adding that increasing the labor force participation rate is a very important. "We are moving forward on this, but it's just very slow," he said. "Monetary policy works with a lag and we have to take that into account as well."
As for economic growth, he said, "I think we'll see things picking up through the year. And so I wouldn't be surprised to see real GDP growing at a rate of above 2.5 percent as we get toward the end of the year. Not what I'd want. I'd like little more."
Fed Chairman Bernanke is scheduled to talk about the economy before the Joint Economic Committee on Wednesday morning—hours before the central bank releases minutes from its April 30-May 1 meeting.
The Fed's next policy meeting is scheduled on June 18-19, with Bernanke scheduled to hold a news conference afterwards.
Fisher said the U.S. needs a rational fiscal policy to help spur economic growth. The Fed is basically underwriting Congress for not doing its job, he argued, saying he's an "equal opportunity basher" of both Democrats and Republicans.
Cheap money has made rich people richer, but hasn't done quite as much for working Americans, he explained.
CORRECTION: An earlier version of this story incorrectly said Dallas Fed President Richard Fisher told CNBC the Federal Reserve should go from "wild turkey" monetary policy to "cold turkey" overnight. Instead, Fisher said the Fed should not go from "wild turkey" monetary policy to "cold turkey" overnight.