WASHINGTON – A Republican plan to extend tax cuts for the rich would add more than $36 billion to the federal deficit next year — and transfer the bulk of that cash into the pockets of the nation’s millionaires, according to a congressional analysis released Wednesday.

New data from the nonpartisan Joint Committee on Taxation show that households earning more than $1 million a year would reap nearly $31 billion in tax breaks under the GOP plan in 2011, for an average tax cut per household of about $100,000.

The analysis, requested by Democrats on the tax-writing House Ways and Means Committee, comes as debate heats up over tax cuts enacted during the Bush administration, most of which are scheduled to expire at the end of this year. Republicans want to extend all the cuts, which would cost the Treasury Department $238 billion in 2011, according to the taxation committee.

President Obama and congressional Democrats want to extend the cuts only for families making less than $250,000 a year and individuals making less than $200,000 — 98 percent of American taxpayers — which would add about $202 billion to next year’s deficit.

Given the soaring national debt, many economists deem both proposals unaffordable. Even some Republicans, including Reagan administration budget chief David Stockman, have urged lawmakers to let all the cuts expire and allow income tax rates to rise to their levels during the Clinton administration.

Obama campaigned on a pledge not to raise taxes for the middle class, however. And with midterm congressional elections in November, few politicians in either party are calling for full repeal.

Both sides are eager to engage in a fight over taxes on the richest Americans on the eve of the election. Democrats see a political advantage in accusing Republicans of holding tax breaks for the middle class “hostage” in order to get tax cuts for the wealthy, though it’s not clear that GOP lawmakers would in fact block extension of the middle-class cuts if they were offered alone.

Republicans accuse Democrats of plotting one of the biggest tax hikes in American history, arguing that raising taxes on wealthy households would punish the very people capable of creating jobs and spurring economic growth.

About half of all small-business income is reported on the individual returns of people making over $250,000 a year, according to the taxation committee’s data.