"Hey! Not my fault. The President believes in 'Do what I say, not what I do.' "

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The intersection of Duke Energy’s interests and its support for the convention is testing Mr. Obama’s pledge to free the party’s gathering from business and lobbyist support.

The situation is a microcosm of a larger issue that Mr. Obama’s campaign has faced. It has tried to balance the president’s longtime pledge to reduce the influence of special interests in politics with his real-world need to raise the huge amounts of money that modern campaigns require, at times in ways that seem to contradict those pledges.

Republicans are accusing the convention organizers of hypocrisy. Some Democrats are saying the White House set itself up for the charges by making a vow that was bound to be difficult to keep and that would risk alienating its business supporters.