Members of the American Medical Association disgruntled over the group's backing of the House health care reform bill have dropped their bid to overturn the endorsement, according to one source inside the group. 

The source told Fox News in an e-mail that some delegates have even become convinced that the bill, which passed by a narrow margin Saturday night, could be good for physicians despite lingering concerns about Medicare cuts. 

Some members were outraged that the group's trustees made the endorsement Thursday without the formal approval of the organization's House of Delegates. 

A vote had been scheduled for Monday on a resolution offered by some members to withdraw the AMA's endorsement of the bill. 

President Obama cited the endorsement of the influential AMA, along with AARP's, in a surprise appearance Thursday in the White House briefing room as he attempted to beat back criticism that the bill would gut Medicare. 

"They're endorsing this bill because they know it will strengthen Medicare, not jeopardize it," he told reporters. "They know it will protect the benefits our seniors receive, not cut them." 

"So I want everyone to remember that the next time you hear the same tired arguments to the contrary from insurance companies and their lobbyists and remember this endorsement the next time you see a bunch of misleading ads on television," he added. 

Fox News' Trish Turner and Major Garrett contributed to this report.