WASHINGTON — A small nonpartisan research center operated by professed “geeks” has found itself at the center of a rancorous $5 trillion debate between President Obama and Mitt Romney.

No white paper or policy manifesto put out during the presidential campaign has proved more controversial than an August study by the Washington-based Tax Policy Center, a respected nonprofit that issues studiously detailed tax analyses.

That study found, in short, that Mr. Romney could not keep all of the promises he had made on individual tax reform: including cutting marginal tax rates by 20 percent, keeping protections for investment income, not widening the deficit and not increasing the tax burden on the poor or middle class. It concluded that Mr. Romney’s plan, on its face, would cut taxes for rich families and raise them for everyone else.

The detailed paper proved kindling for a political firestorm. Mr. Romney criticized the center as performing a “garbage-in, garbage-out” analysis and his campaign accused it of partisan bias. The Obama campaign used the center’s numbers to argue that Mr. Romney had proposed a $5 trillion tax cut. Economists jumped on the bandwagon too, flinging analyses back and forth and picking apart the projections and assumptions in the report.