Republicans would be wise if they used the process. Tax cuts for the rich are popular; all government spending has constituencies that will be upset if they are cut. Thus any change towards fiscal sanity will upset some group or another. By negotiating a piece at a time Republicans will get rolled.
Rather they should insist that the budget process be followed. The House has a budget on the table and they should insist that Harry Reid and Barrack Obama do the same.
Only by forcing Reid and Obama to do that will they avoid being rolled and catching blame for whatever happens.