Washington (CNN) -- They are losing the battle over higher taxes on the wealthy, so now Republicans are threatening a political war next year when it comes time to raise the nation's debt ceiling. With cracks appearing in their anti-tax facade and polls showing most Americans favoring President Barack Obama's stance in the fiscal cliff negotiations, GOP legislators are starting to advocate a tactical retreat to fight another day. Conservative Sen. Lindsey Graham, R-South Carolina, promised the newly re-elected Obama "one hell of a fight" next year if the president forces through his plan for high-income earners to pay more taxes without agreeing to substantive steps to reduce the nation's chronic federal deficits and debt.
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NEW: White House, Republicans exchange counteroffers; Boehner, Obama talk on phone
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NEW: Graham promises "one hell of a fight" over debt ceiling hike unless deficit cut
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The White House challenges GOP leaders over who lacks specifics
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Polls show most Americans back the president on raising taxes on the rich
He and Boehner want @placeholder to take some of the political heat for proposing cuts to entitlement programs and other government spending.