The federal government should begin drafting a plan to privatize large mortgage lenders Fannie Mae and Freddie Mac, the Senate Budget Committee's top Republican said Monday.

Sen. Judd Gregg (R-N.H.) said that the federal government's effort to keep the embattled lenders on "life support" siphons away too many tax dollars. 

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"We should have a game plan for privatizing those institutions and moving them off the federal books," he said on CNBC. " Basically, Fannie and Freddie...the fact that we're keeping them on life support at the cost of billions of American taxpayers' dollars is a huge mistake."

Gregg's remarks come as concerns about Fannie and Freddie heightened after the government lifted the $400 billion investment cap on the two companies on Christmas Eve. The Treasury Department recognized the government would likely lose more than that sum due to its commitment.

Before 2008, Fannie and Freddie operated as a private government-sponsored enterprise, The federal government bailed out the companies after many consumers defaulted on their mortgages during the housing crisis.

Critics blamed Fannie and Freddie for accelerating sub-prime lending that was a main contributor to the housing collapse.

Gregg suggested that the government could use so-called "resolution authority" -- should Congress pass financial regulatory reforms with it included -- to privatize Fannie and Freddie. That power would allow the government to seize and restructure large, troubled firms.

But House Financial Services Committee chairman Barney Frank (D-Mass.) said last week that the renwed government commitment to the firms is part of an effort to transform them into "public policy instruments of the government." 

Frank indicated that the government could use the companies to help buoy consumers who are struggling to make their mortgage payments.