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"We're willing to discuss that, but it needs to happen one way or another," the Michigan Democrat said. "There are various ways to bring it up, but it should not be left to the last minute and it should not be used as a bargaining tool."
One of those ways — passing an extension through the Appropriations Committee — may be unlikely. Rep. Jo Ann Emerson, who chairs the House Appropriations Subcommittee on Financial Services and General Government, said she "can't envision" such an "expensive" measure going through the committee.
"It makes sense to do it in the super committee," the Missouri Republican said.
Extending unemployment insurance has traditionally had strong bipartisan support, particularly during recessions or other periods of high unemployment. But in the past several years Republicans have defied demands for unpaid-for extensions.
Last year, then-Sen. Jim Bunning (R-Ky.) launched a one-man filibuster of such a bill. Initially, his GOP colleagues harshly criticized him, fearing an angry backlash from voters. And while there was indeed an outcry, Republicans did not feel the kind of political pain many had expected.
Rep. Joe Crowley, a member of the Ways and Means Committee, said it would not be "beyond the pale" for Republicans to drag out the issue to Christmas or hold it up entirely.
"I don't think anything is beyond the pale anymore. I think anything is possible," the New York Democrat said. "If they want to play Scrooge, they're welcome to it."
For their part, rank-and-file Republicans said although they do expect an end-of-year battle, the issue hasn't been widely discussed.
"It's going to be a heavy lift. It's going to be a difficult one," said Republican Study Committee member Rep. Jason Chaffetz (Utah). "It's not something we've talked about recently. I haven't heard a peep about it."
Rep. Kevin Brady, a senior member of the Ways and Means Committee, said the silence on the issue likely has to do with Members waiting for the super committee to move.
"Right now the super committee is sucking up all of the oxygen" the Texas Republican said. "I think it's an indication that the super committee has such a broad jurisdiction that it's impacted the thought process of what needs to be done by the end of the year."
He added, "I'm sure it's on our radar; I don't know how much."
Jessica Brady and John Stanton contributed to this report.