The republicans are having trouble as most of them declare they cannot vote for a tax increase. What I find puzzling is that they voted overwhelmingly FOR the currently imminent tax increase. The deal to raise the debt ceiling had 2 mechanisms for long term budget prudence.
1. A special committee 3 House republicans, 3 House democrats, 3 Senate republicans, and 3 Senate democrats was created and tasked with bipartisan recommendations for deficit reductions.
2. A set of spending cuts (the "sequester") (and the Bush temporary tax cut expiration via acceptance of CBO numbers) were agreed as required in the event of the failure of the bipartison committee (which indeed failed to have any consensus).
In addition, deficit reduction calculations were done with the assumption that the Bush temporary tax cuts would expire as planned and approved by Congress.
A vote to raise the debt ceiling WAS a vote for the current plan known as the "Fiscal Cliff". 174 republicans and 94 democrats in the House voted for that resolution.
I am sure that republicans thought they would win all the elections and get to re-write the previously passed legislation, but they didn't win and they did vote for the ceiling increase.
Congress voted for a TWO YEAR extension of the temporary Bush Tax cuts in 2010. With the expiration timed for after the 2012 elections. Republicans overwhelmingly voted for the bill. A majority of democrats voted against the bill.
Now the republicans can easily argue that the temporary tax cut was temporary and rolling it back is not an increase. But they have been arguing for a long time that the tax rate increases are unacceptable and that the temporary cuts have always been intended for permanence. That simply is not fiscally prudent.