Republicans should not consent to higher tax rates to reach an ostensibly non-partisan compromise on deficit reduction.   The main reason is that Congress will very likely use a good chunk of any tax increase  to sustain excessive spending.  To elaborate:

If federal spending is cut by $1, the direct effect is to reduce the federal deficit by $1.  The indirect effects are uncertain in magnitude and perhaps in direction.  Some people in general and economists in particular believe that reduced spending will hurt the economy and increase other federal spending (e.g, for unemployment benefits) and/or reduce tax collections.  Other people and economists believe that reduced spending will help the economy and reduce other spending and/or increase tax collections.  Academic and other researchers try to estimate the effects of past spending cuts and predict what would happen now.  The results are subject to significant uncertainty.

If federal taxes are increased by $1, the direct effect is to reduce the deficit by $1.  The indirect effects depend on the effect of the tax increase on economic activity.  While the effects are uncertain in magnitude, it is highly probable that tax increases would reduce economic growth, increasing other government spending and reducing tax collections.  Academic and other researchers again try to estimate the effects of past tax increases and predict what would happen now.  The results likewise are subject to significant  uncertainty.

If, however, taxes are increased as part of a political compromise to reduce the deficit, it is entirely plausible that spending will not be reduced as much as would ultimately be the case without tax increases.   In other words, Congress will use some portion of any tax increase to sustain spending.  Other things being equal, a $1 increase in taxes would then reduce the deficit by less than $1.

The connection between taxes and government spending has been researched with historical data, as usual with less than definitive results.  My own strongly held view is that federal spending is much too high, that marginal tax rates are too high, and that any increase in taxes will in significant part finance spending that should be cut.