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“We can act, carefully and responsibly, to prevent a potential act of genocide,” Mr. Obama said. “These terrorists have been especially barbaric toward religious minorities, including Christians and Yazidis, a small and ancient religious sect.”

Iraqi Christians have been pleading with the administration to take action against IS. But some progressives are concerned that humanitarian aid will lead to an open-ended military commitment.

“The world is watching, and genocide must not be used as a fig leaf by war hawks to expand U.S. military involvement throughout the region,” Mr. Chamberlain said.

But Sen. John McCain, Arizona Republican, said that the president’s plan to fix the humanitarian crisis is not a coherent strategy for the growing problem.

“The president made it clear this was to avert the humanitarian crisis and to protect American military personnel,” Mr. McCain said on CNN’s “State of the Union.” “That’s not a strategy; that’s not a policy. That is simply a very narrow and focused approach to a problem that is metastasizing as we speak.”

Other critics on the right say the president is already indulging his base by ordering a small, narrow military effort that fails to encompass a strategy for defeating IS.

“Every White House effort is small because it’s not part of a larger strategy to defeat the enemy,” said Danielle Pletka, vice president for foreign and defense policy studies at the conservative American Enterprise Institute. “As to how it plays, that’s up to the president. He has no desire to persuade and, as a result, will not.”

Some Democrats are waiting to see whether Iraqis can form a new central government that is more inclusive, saying it should be a condition of U.S. military aid. Administration officials say they are hopeful that a new government will be formed, without Prime Minister Nouri al-Maliki, within days.

“I support President Obama’s decision to send humanitarian and military aid,” said Rep. James E. Clyburn, South Carolina Democrat. “Ultimately, there is no substitute for political accommodation between all elements of Iraqi society to join together and expel the [IS] extremists from their country. In the meantime, though, while I agree with the president that American ground troops should not return to Iraq, we must assist the Iraqis in their efforts to stop militant gains and prevent humanitarian catastrophe.”

Whatever the political fallout, observers say the president’s predicament is a far cry from the reassurances he gave Americans in December 2011, when he said the U.S. was leaving Iraq in a good position for the future.

“Iraq’s future will be in the hands of its people,” Mr. Obama said at Fort Bragg, North Carolina, as he withdrew the last of the U.S. troops from Iraq. “America’s war in Iraq will be over. Iraq is not a perfect place. It has many challenges ahead. But we’re leaving behind a sovereign, stable and self-reliant Iraq, with a representative government that was elected by its people. We’re building a new partnership between our nations.”