From a Mitch McConnell statement Wednesday:
The President claims to want a balanced approach to solve our problems. And now that he has the tax rates he wants, his calls for 'balance' mean he must join us in our efforts to achieve meaningful spending and government reform. We have an immediate opportunity to act: the debt ceiling. Washington's credit card has reached its limit again, and the Senate majority must act on legislation early in February--rather than waiting until the last minute, abdicating responsibility and hoping someone else will step in once again to craft a last-minute solution for them. Once the Senate passes bipartisan legislation, we can conference with the House on a solution. But this time the entire Senate must have an opportunity to act.
Emphasis added. Not only are Republicans closing the door on more tax revenues than they already provided Obama. And not only are they demanding unpopular spending cuts as their price for raising the debt limit. If you read between the lines, they're actually insisting that Democrats put together the spending cuts themselves.
They don't want their prints on any specific entitlement cuts until Democrats have proposed them first. In that sense this is just like the fiscal cliff fight. Except the consequences of blowing through the other side of the debt limit are much more grim.