The Democrats want to raise revenue and the Republicans want to reform entitlements. Those goals would seem to be easily reconciled — just do some of each, or even lots of each. But it only seems that way because we don’t often think about why the parties want these things. Simply (and surely somewhat too simply) put, the Democrats want more money so that the entitlement system doesn’t have to be reformed, while the Republicans want to reform the entitlement system so that the government doesn’t have to take more of the country’s money or take up even more of the economy. That means that doing some of each, let alone lots of each, doesn’t give both parties what they want, it gives both parties what they are desperately trying to avoid.
It is not really in either side's interest to compromise: The left would like to only raise taxes on "the rich" but don't really care if everyone gets hit--especially if they can blame the Republicans for it. The Republicans would rather have the taxes hit everybody since otherwise, there would be no leverage to get the economically harmfull rates on the high incomes brought back down.
The place where the Republicans have real leverage is on the debt limit. If they don't raise it then 31% of all federal spending will have to be cut. This is roughly the amount of spending on the discretionary side of the budget. If no agreement is made, then entitlements will have to be cut.