"There is no question that it is very challenging," said an official from one, who spoke on condition of anonymity because he is not authorized to speak publicly on behalf of the organization.
The groups argue that inaction will undermine American credibility in limiting the development and use of weapons of mass destruction with a direct impact on Israel's security, particularly as it relates to Iran and its nuclear program.
Israel regards Iran as an existential threat, and preventing Tehran from developing nuclear weapons is its primary national security concern. Iran says its program is for peaceful purposes.
Lobbyists also acknowledge that a U.S. military strike could risk Israel becoming a retaliatory target of Syrian-backed Hezbollah or other groups acting on Assad's behalf. But they say that risk is smaller than the risk of letting Assad go unpunished.
"This critical decision comes at a time when Iran is racing toward obtaining nuclear capability," AIPAC said in its statement. "Failure to approve this resolution would weaken our country's credibility to prevent the use and proliferation of unconventional weapons and thereby greatly endanger our country's security and interests and those of our regional allies."
The Anti-Defamation League urged Congress to "act swiftly to add its voice to hold (Assad) accountable for the wanton slaughter of his own citizens."
"Any nation that violates international norms and obligations which threaten the peace and security of the world must face the consequences of those dangerous acts," it said.
Obama and his aides have gone out of their way to court the support of the American Jews by drawing parallels between Syrian President Bashar Assad's use of poison gas and the gas chambers of Nazi Germany.
Visiting the Great Synagogue of Stockholm on a trip to Sweden last week, Obama alluded to the connection while paying tribute to Raoul Wallenberg, the Swedish diplomat credited with saving at least 20,000 Jews during the Holocaust.
"Because he refused to stand by, Wallenberg reminds us of our power when we choose not simply to bear witness, but also to act," Obama said.
Secretary of State John Kerry has invoked the phrase "never again," a direct reference to international vows to prevent a repeat of the Holocaust, and even compared Assad to Adolf Hitler, something that even the pro-Israel groups backing the administration have avoided.
Despite winning universal condemnation of Assad for using chemical weapons, the administration has found its arguments are not convincing skeptical lawmakers and their war-weary constituents that military action is a moral imperative.
Officials with several pro-Israel groups say they are encountering the same problem, which is compounded by pure political motivations, especially among Republicans, for opposing Obama's request.
They said they will continue to lobby AIPAC is bringing some 250 pro-Israel activists to Washington in the coming days to push for the authorization but they have also told the White House that only a powerful and direct personal appeal from Obama himself is likely to have an impact.
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Associated Press writer Matthew Lee contributed.
