A solution to the deficit problem?

I have heard of a very simple approach to attack the deficit problem.
The Democrats don't want the rich to escape contributing a larger share of the tax burden.
The Republicans are against any kind of tax increase - particularly for the rich.
And eliminating deductions that are available mostly to the rich doesn't get much traction, either. 
Are these points unreconcilable? I don't think so.  Imagine a system where a sliding scale of tax rates applies, with more or less the same rates as today.
The wrinkle is that the everybody has a limit to the total amount of deductions that they can take, whatever the kind.  In much the same way that the interest on the mortgage of a second house isn't deductible, simply construct a rule that caps the deductions of any kind at a set level, perhaps on a sliding scale according to income.
Thus, the rates could be as they are now, but it would prevent the ultra rich from having as many tax escape routes as they have now.