Senate Finance Committee ranking member Chuck Grassley (R-Iowa) also discouraged holding separate votes on middle-class tax cuts and those in the higher-income brackets saying, "we shouldn't raise taxes during a recession."
If necessary, the Senate could take votes on several different middle-class tax cut packages "to show the American people that we support the middle class and that we do not believe that, if we're going to continue to talk about debt and deficit, we can walk away from how much these tax cuts cost."
Most Democrats and the White House have said their top priority is ensuring that the middle-class tax cuts are extended, whereas Republicans have been pushing for an extension of all the tax breaks.
So far, Senate Democrats haven't produced a tax package, beyond what Reid called for Thursday afternoon, to be considered during the lame-duck session.
There are several other major tax issues, including the alternative minimum tax and the estate tax, which expired at the end of 2009, that haven't been ironed out by Democrats.
House Democrats announced earlier Thursday that they will hold a separate vote during the lame-duck on a proposal to extend the middle-class tax cuts only, Majority Leader Steny Hoyer (D-Md.) said Thursday.