That's a question directed mainly at Republicans as a solution to the debt ceiling negotiations. They aren't interested in simply raising the debt ceiling like they have every time before. Now that they have some power they want something in return for raising it, mainly a lowering of the deficit.
The main solution Republicans have for reducing the deficit is reducing spending. That's fine as far as it goes. But even Republicans don't seem willing to cut enough spending to totally balance the budget. So that leaves the other part of the equation, revenue increases. Obviously they don't want to raise taxes in order to increase revenue. Their logic is that it will hurt businesses, and thus the economy (which is a fair point during the current economic climate). (Though its interesting that they don't seem challenge the idea that raising taxes would raise more revenue.)
Following their logic on tax increases, they like tax cuts because they believe it would help businesses. Not only that, Republicans also believe that tax cuts increase revenue. So as a solution to both the debt ceiling and the poor economy why not ask Obama for more tax cuts? If their theory is correct, businesses will invest the money they are saving from the cut, which will grow their business and allow them to hire more employees. That would be great for the economy. And since those tax cuts will also bring in more revenue they will also lower the deficit. According to their logic its a win-win, right?
Taxes are really low right now, as are revenues. And just a few years ago we extending the Bush tax cuts. But I'm not sure why (if Republicans believe in the economic policies they propose) they shouldn't be arguing for even more tax cuts. Not only would their constituents like it, they could use it as leverage against Obama. If they were to come out strong for more tax cuts and make their typical argument about cuts raising revenue and thus decreasing the deficit and Obama didn't go for it they could bash him at every turn for not wanting the cuts. Yet as far as I know the only thing Republicans want out of the debt ceiling deal is a lot of spending cuts and no tax increases. Is there any Republican that can explain to me why they don't want more tax cuts? What am I missing?