The Republicans will agree to a tax rate rise for those making above $500,000 a year, a restriction on some loopholes, and raising the capital gains rates for those making above a million a year. This will allow them to say that they haven't hurt the mom and pop businesses and that they are not just for the extremely wealthy.
The Democrats will agree to cut back on some entitlements (whether they make an end run around these is another matter). This will allow them to appear as if they have won on the tax front and are serious about cutting the deficit as well.
Both sides get to save face, and the national debt will continue to increase.
That's why they call it politics.