By Gabriel Debenedetti

WASHINGTON (Reuters) - As President Barack Obama's team faces one of its toughest lobbying challenges in urging Congress to approve U.S. military action in Syria, the advocacy group dedicated to promoting the president's agenda is staying quiet.

In recent months, Organizing for Action - the non-profit group that grew out of Obama's 2012 re-election campaign - aggressively defended the president's healthcare overhaul, his call for new immigration policies and his unsuccessful push for new gun-control laws.

But in the debate over whether to intervene in Syria - which has given many congressional Democrats the uncomfortable choice of supporting a military strike they don't want or rejecting a plea for action from the Democratic president - OFA has remained on the sidelines.

That's by design, OFA executive director Jon Carson said on Thursday, adding that the group does not intend to send supportive emails or lobby on the issue.

"OFA supports President Obama and the agenda that Americans voted for on November 6, but we don't always actively organize around every issue, and the debate in Congress over the Syria vote is not one that OFA is planning on organizing around," Carson said.

OFA did not respond to questions about whether its silence on Syria demonstrated that its focus is Obama's domestic agenda.

Syria "doesn't fall within the OFA focus," said John Morgan, a Florida-based lawyer who donated $50,000 to the group in the first quarter of 2013. "This is not the president's agenda. It has fallen to him spontaneously."

RISK OF ALIENATING SUPPORTERS

A donor to the group who asked not to be identified said that OFA's stance on Syria reflected the "no-win" nature of many foreign policy issues.

"Obama's goal in getting elected, and our goal in electing him, wasn't dealing with this nightmare in Syria," the donor said.

Because there is a divide on Syria within Obama's Democratic Party on the issue, the group risks "alienating half its members" if it weighs in, the donor added.

Obama's team had hoped to be promoting proposals to revamp the nation's immigration laws and other measures now. But those goals have been sidetracked by the debate over whether the United States should retaliate against Syrian President Bashar al-Assad because of his alleged use of chemical weapons last month in an attack near Damascus that the White House says killed more than 1,400 people.

On Thursday, Obama canceled a California trip planned for next week so that he could stay in Washington and focus on Syria after he returns from the G-20 economic summit in Russia late Friday.

Since its launch in January, OFA has sent out e-mails and hosted events nationwide to promote the administration's plans on healthcare, immigration, climate change, gun control and education. Obama's positions on each of those issues have broad support among Democrats.

Some critics have questioned the group's effectiveness, noting that its ads promoting gun control in light of the massacre of 26 children and adults at a Connecticut school did not seem to help Obama in a failed effort to get gun legislation through Congress.

OFA is still widely viewed as a potentially formidable advocacy group, largely because it raised more than $13 million during its first six months, mainly from Democratic donors.

(Editing by David Lindsey and Cynthia Osterman)