Of course what the President do on his own is limited, without more funding. Well, now some Senators have introduced an actual bill to do something about it:
S.2145, the "Middle East Refugee Emergency Supplemental Appropriations Act" of 2016, would provide $1 billion in funds to resettle approximately 100,000 more refugees in the US, and improve conditions in refugee camps in Jordan and the region. And it was introduced by a Republican and a Democrat together, which gives it a shot of rising above the hyper-partisan nature of most votes in the Senate. But so far, all of the additional cosponsors have been Democrats.
The Senate repeatedly passed emergency supplemental appropriations to fund the Iraq war, totalling hundreds of billions of dollars. That war caused a large part of this refugee crisis, because the extremist groups who infiltrated and took over Syria's civil war, and have lengthened it and made it so unresolveable, were nearly all products of our Iraq invasion. ISIS, Al-Nusrah, and so on - they were created by people who recruited in Iraq, trained in Iraq, gained experience and built networks in Iraq, and then came from Iraq to Syria when the opportunity presented itself. Surely the same Senate that spent hundreds of billions to put tens of millions of civilians in crisis and misery, can vote for just $1 billion to rescue some of them. (they should do more, but this is a good start)
Look at that list of cosponsors. If one of your Senators is on it, call them and thank them! They've all been getting some calls from anti-immigrant people upset at the thought of resettling refugees. And whichever of your Senator(s) aren't on the list - call them and ask them to cosponsor!
Especially if they're a Republican, because getting a couple of additional Republican supporters is probably what will make the difference in whether this passes or not.