On Friday, the issue reached the highest levels as President Bush and Turkish Prime Minister Recep Tayyip Erdogan talked by telephone about their opposition to the legislation, which is to go before the House Foreign Affairs Committee on Wednesday.
The dispute involves the deaths of hundreds of thousands of Armenians during the waning years of the Ottoman Empire.
Armenian advocates, backed by many historians, contend the Armenians died in an organized genocide. The Turks say the Armenians were victims of widespread chaos and governmental breakdown as the 600-year-old empire collapsed in the years before Turkey was born in 1923.
Armenian supporters of the congressional measure, who seem to have enough votes to get approval by both the committee and the full House, have also been mustering a grass-roots campaign among the large diaspora community in the United States to make sure that a successful committee vote leads to consideration by the full House.
One interest group, the Armenian National Committee of America, has engaged about 100,000 supporters to call lawmakers about the issue, according to Executive Director Aram Hamparian.
Similar measures have been debated in Congress for decades. But well-organized Armenian groups have repeatedly been thwarted by concerns about damaging relations with Turkey, an important NATO ally that has made its opposition clear.
Lawmakers say that this time, the belief that the resolution has a chance to pass a vote by the full House has both Turkey and Armenian groups pulling out all stops to influence the members of the committee.
"The lobbying has been the most intense that I have ever seen it," said the bill's sponsor, Rep. Adam Schiff, D-Calif.
Though the largely symbolic measure would have no binding effect on U.S. foreign policy, it could nonetheless damage an already strained relationship with Turkey.
After France voted last year to make denial of Armenian genocide a crime, the Turkish government ended military ties.
Many in the U.S. fear that a public backlash in Turkey could lead to restrictions on crucial supply routes through Turkey to Iraq and Afghanistan and the closure of Incirlik, a strategic air base in Turkey used by the United States. Lawmakers have been hearing arguments from both sides about those concerns.
The Turkish government has been holding back from public threats while making clear that there will be consequences if the resolution is passed.
"There will be a backlash and no government can be indifferent to that," says the Turkish ambassador in Washington, Nabi Sensoy.
But Armenian groups charge that behind the scenes, Turkey has been much more clear.
"Turkey has been threatening every sort of doomsday scenario," says Hamparian. "We have been saying that Turkey would harm itself more than the United States if it carries through with these threats."
Turkey argues that the House is the wrong institution to arbitrate a sensitive historical dispute. It has proposed that an international commission of experts examine Armenian and Turkish archives.
In the meantime, the Turkish embassy has been in close contact with lawmakers and is using prominent U.S. lobbyists.
"I have redoubled my efforts," says Sensoy. Turkish lawmakers have also been manning the phones to congressional offices.
According to one congressional aide, Turkey's military chief, Gen. Yasar Buyukanit, has been calling lawmakers to argue that a vote will boost support for Islamists in Turkey. The aide spoke on condition of anonymity because of the sensitivity of the issue.
The Bush administration has been telling lawmakers that the resolution, if passed, would harm U.S. security interests.
Gordon Johndroe, a White House spokesman, said Friday that Mr. Bush believes the Armenian episode ranks among the greatest tragedies of the 20th century, but the determination whether "the events constitute a genocide should be a matter for historical inquiry, not legislation."
White House staff have also spoken with aides to House Speaker Nancy Pelosi, D-Calif., in the hope that she will stop the measure from coming to a vote.
"The administration has reached out to the speaker's office and made our position clear," he said. "We'll see what happens."
By Associated Press Writer Desmond Butler