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“All charities will lose revenue, but I expect that educational and health organizations will be hit the hardest, while religious and social-service organizations will be affected the least, as their donor base is skewed toward lower-income households who are less likely to enjoy tax credits to begin with,” he said in a statement.

But others point out that Mr. Obama’s proposed budget for fiscal 2013 included a proposal to limit charitable giving deductions at 28 percent, rather than the current 35 percent, for those making $250,000 or more.

The White House said in February that 80 percent of overall contributions “wouldn’t be affected at all” because the money comes from families who earn less than $250,000, an argument disputed by many charities.

“The president is sending mixed messages to the charitable community,” Sue Santa, senior vice president of the Philanthropy Roundtable, said in statement at the time. “On one hand, he wants to limit the charitable deduction. On the other, he wants millionaires to continue to give to charity while also paying higher taxes.”

Speaker John A. Boehner, Ohio Republican, said this week that Mr. Obama was frustrating their negotiations by moving the goal posts. He said Mr. Obama in 2011 favored the GOP’s plan to bring in revenue through closing deductions and loopholes.

White House officials say the president supported the idea as part of an overall plan to update the tax code, and that Mr. Obama envisioned raising tax rates on the top 2 percent of wage earners if Congress couldn’t complete the changes to tax law by the end of this year.