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“I think it is to his advantage and the country’s advantage to have Congress buy into that,” Senate Minority Leader Mitch McConnell said before joining other Republican and Democratic leaders in the Oval Office on Tuesday for a meeting with Obama.

None of the leaders spoke to reporters as they left the White House.

However, an aide to House of Representatives Speaker John Boehner said the Ohio Republican expressed support for efforts to increase the effectiveness of the Iraqi security forces and for equipping the Syrian opposition. Boehner also said he would support the deployment of U.S. military personnel to Iraq in a training and advisory role and to “assist with lethal targeting” of Islamic State leadership, according to the aide, who spoke only on condition of anonymity because he was not authorized to discuss the private meeting by name.

In a shift for a war-weary nation, new polls suggest the American people would support a sustained air campaign. A Washington Post-ABC News poll released Monday showed 71 per cent of Americans support air strikes in Iraq, up from 54 per cent just three weeks ago. And 65 per cent say they support extending air strikes into Syria.

Congress heads back to Washington this week—now is not the time to be cynical about what they can accomplish. pic.twitter.com/rUSFuU59UZ — Barack Obama (@BarackObama) September 6, 2014

Taking that latter step would raise legal and geopolitical issues that Obama has long sought to avoid, particularly without formal congressional authorization.

Unlike in Iraq, Obama would not be acting at the invitation of a host government. However, some international law experts say air strikes could be justified as a matter of self-defence if Obama argues the Islamic State group poses a threat to the U.S. and its allies from inside Syria, whose government is unwilling or unable to stop it.

Another possibility: Although the U.S. has said it will not co-ordinate with Assad, his government could give back-channel consent to American attacks.

Obama would still have to contend with the notion that American air strikes against the Islamic State militants were actually helping Assad, who has overseen Syria’s bloody civil war. The U.S. has long called for Assad to leave power, and the Islamic State group is one of the groups inside Syria that is seeking to oust him.