But Hamparian was quick to say that many Republicans, including likely House Majority Leader Eric Cantor (R-Va.) and GOP Whip Kevin McCarthy (R-Bakersfield), support the resolution.
"We've always been fortunate as a community to have friends on both sides of the aisle," Hamparian said.
The legislation by Rep. Adam Schiff (D-Burbank) has stalled because of opposition from Turkey, whose leaders see the resolution as divisive and who say its passage would strain U.S. diplomatic relations with an important regional ally.
On Wednesday, Schiff said support for the measure has been bipartisan, though it has been much stronger on the Democratic side of the aisle.
He added that he is seeking to lock down more support.
"We will move the resolution forward just as soon as we're confident we have the votes," he said.
If that doesn't happen during the current lame-duck session, Schiff said he would reintroduce the resolution in the new Congress.
He said the United States needs to acknowledge the genocide in order to have the moral authority to act or speak out when other atrocities occur around the globe. In addition, he said survivors are still among us.
Time is also of the essence as survivors of the atrocities continue to grow older, he said.
"There is a sense of urgency about recognition of the genocide in their lifetime," Schiff said.
While the resolution is largely symbolic, Hamparian has said it has implications for the long-term future of Armenia. At a Sept. 16 ANC banquet in Glendale, Hamparian said the point of the resolution is not merely to seek the truth for the truth's sake.
"We are seeking truth for the sake of justice," he said. "We are seeking justice for the sake of security."