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Democrats point out that the president did raise about $1 million two weeks ago in Miami at a high-priced event aimed in part at Jewish donors. Mr. Cohen, the Philadelphia host who raised $6.1 million for Mr. Obama in 2008, declined to comment.

The Obama campaign has emphasized its early success attracting a large number of small donors, rather than events like the one at the cable executive’s home, where supporters paid $10,000 just to get in the door and $35,800 for “premium dinner seating.”

“We measure our success not in dollars but in people,” said a statement from the campaign signed “Barack” and emailed to millions of people.

The push for small donors has included a video pitch by the president, taped at the White House, offering “dinner with Barack” and Vice President Joseph R. Biden for four people whose names will be drawn from a pool of supporters.

The solicitation, coupled with a DNC-organized meeting March 7 with high-priced donors in the Blue Room of the White House, spurred criticism from government watchdogs that Mr. Obama is exploiting the executive mansion for fundraising.

Melanie Sloan, head of Citizens for Responsibility and Ethics in Washington, called the events “unseemly,” but she also said they are legal.

Federal election law says federal employees, including the president, cannot solicit campaign donations “while in any room or building occupied in the discharge of official duties by an officer or employee of the United States.”
That restriction doesn’t cover the private residence portion of the White House, though it’s not clear in which room the video was recorded.

White House officials also claimed that the pitch is technically not a fundraising appeal, because the president doesn’t explicitly ask for money. Anyone can sign up for the raffle, although the campaign wants donations of at least $5. The president’s video, taped by a DNC crew, is accompanied by a form in which supporters can check boxes to donate from $5 to $700 to the campaign.

White House officials pointed to video clips of other presidents who have used footage of the White House in campaign ads, including Republicans Ronald Reagan and George W. Bush. Mr. Bush did use video of the White House in an campaign ad that didn’t appeal for money. As president, Bill Clinton also was the target of complaints about selling access to the White House for campaign cash.

Mr. Obama, who once supported the public financing of presidential elections, shattered fundraising records in 2008 by raising about $750 million. In the first half of 2007, he raised $59 million.

There have been suggestions that he will try to raise $1 billion for his re-election, although campaign officials have been downplaying that sum.