Poll: Six in 10 voters favor across-the-board spending cuts

The poll's results followed passage in the House and Senate of a last-minute budget deal that consisted primarily of tax hikes to avert the “fiscal cliff." The debt deal raises $620 billion in new revenue, but lacks large cuts.

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Those cuts may yet materialize. Washington is set for another bruising round of negotiations in late February over the debt ceiling and sequestration, the latter of which was delayed by the debt deal. 

Republicans are vowing to use the leverage afforded by those issues to win concessions from Democrats and the administration on spending. Sen. Pat Toomey (R-Pa.) called on fellow Republicans to “tolerate a temporary, partial government shutdown” as a tactic to pressure the administration. 

President Obama sent his own shot across the GOP's bow Tuesday night, warning Republicans that he "will not have another debate with this Congress over whether or not they should pay the bills that they've already racked up through the laws they passed."

 The consequences would be “catastrophic — far worse than the impact of a fiscal cliff,” he warned.