Last year the United States accepted only 31 Syrian refugees, Sen. Dick Durbin, D-Ill., said at a Senate hearing last week.
The Office of the U.N. High Commissioner for Refugees, or UNHCR, wants to resettle about 30,000 particularly vulnerable Syrian refugees in fiscal 2014.
The United States, Durbin said, typically accepts about half of resettled refugees. The U.S. State Department has told the UNHCR the United States is ready to accept referrals but has made no commitments.
About 135,000 Syrian refugees have applied for asylum in the United States.
Durbin said "overly broad immigration bars" in the United States are preventing legitimate Syrian refugees from reaching the United States but President Obama has the power to do something about it.
"The ongoing civil war in Syria has created the world's worst humanitarian and refugee crisis since the Rwandan genocide and perhaps since World War II," Durbin, the Senate majority whip and chairman of the Senate Judiciary Subcommittee on the Constitution, Civil Rights and Human rights, said in a statement. "Of the nearly 2.3 million Syrian refugees that have fled the bloody civil war, nearly half are children.
"While the United States has led the world in resettling and providing humanitarian assistance to refugees from conflicts around the globe, we've not done enough to address the current Syrian crisis. In particular, the Obama administration should use the authority Congress gave it to exempt deserving Syrians from the overly broad immigration bars that prevent legitimate refugees from finding safe haven in the United States."
Durbin said people may disagree on how to resolve the Syrian conflict, but "there should be no disagreement that it is a moral and national security imperative to do all we can to help alleviate the suffering of innocent Syrian refugees."
Even tiny Lebanon, which has its own factions constantly on the verge of violence, "is hosting more than 860,000 Syrian refugees, more than 20 percent of Lebanon's population," Durbin said. "This is equivalent to the United States accepting 60 million refugees."
Sen. Ted Cruz of Texas, the ranking Republican on the panel, said he was particularly concerned about Christian refugees in Syria.
In prepared testimony for Durbin's committee, Anne Richard, assistant U.S. secretary of state for population, refugees, and migration, noted the violence has not been restricted to Syria.
"At times, violence from the Syria conflict has spilled across borders into Turkey, Lebanon and Jordan and has aggravated already heightened sectarian tensions in Lebanon," she said.
"The government of Turkey estimates that it now hosts more than 700,000 Syrians; more than 200,000 of these refugees live in 21 camps. While photos of Syrian refugees in camps in Turkey or Jordan are often used to illustrate the refugee situation, most refugees in the region -- more than 80 percent -- do not live in camps and instead have found shelter in local communities and cities."
That has a devastating effect on communities over the borders.
"The impact on many communities across the region is overwhelming. Schools have moved to double-shifts to accommodate Syrian children," Richard said. "Hospital beds are filled by Syrian patients. Rents have risen and wages have fallen as a result of the competition for housing and jobs. There are water shortages in Jordan and Lebanon."
In his own prepared statement to the subcommittee, Sen. Patrick Leahy, D-Vt., also condemned the barriers to accepting Syrian refugees in the United States and called on Obama to act.
"The number of displaced Syrians, particularly women and children, is staggering and will continue to grow," Leahy said. "The world is very grateful to Syria's neighbors, who have opened their arms to hundreds of thousands of refugees. But we must also work here in the United States to fulfill our commitments to the Syrian people
"I am proud that the U.S. has provided over $1.3 billion in humanitarian aid since the beginning of the crisis, and has opened its doors to 90 Syrian refugees thus far" in the three years of civil war, Leahy said, "but we can -- and must -- do more. One considerable hurdle to our refugee assistance efforts are the overbroad 'Terrorism-Related Inadmissibility Grounds' -- or TRIG bars -- found in existing immigration law, as well as the Department of Homeland Security's current interpretation of 'material support' to include even 'de minimus' support. That interpretation has led to perverse outcomes including barring otherwise eligible refugees because they have sold flowers or other commercial goods to customers who happen to be affiliated with a banned group."
Leahy said it's "time the administration took action to end it."
Durbin sounded much the same theme.
He criticized the "overly broad bars in our immigration law that exclude any refugee who has provided any kind of support to any armed rebel group, even a group supported by the United States. This would prevent a Syrian who gave a cigarette or a sandwich to a [Western supported] Free Syrian Army soldier from receiving refugee status, despite the fact that the United States is providing assistance to the FSA. On a bipartisan basis, Congress has given the executive branch authority to create exemptions to these immigration bars for deserving refugees."
Part of the concern in the United States about the Syrian opposition is that jihadists from around the region have flooded into Syria to join the civil war, seeking to establish an Islamic government to replace the brutal, but secular regime of Bashar Assad.
Last week, opposition factions spent as much time fighting each other as fighting the regime. Moderate rebel factions united in something called the Mujahedin Army, including the Free Syrian Army, routed an extremist group affiliated with al-Qaida, the Los Angeles Times reported.
Early last month, the Obama administration temporarily suspended the delivery of non-lethal aid to moderate rebels in Syria. The New York Times said U.S. officials acted after warehouses of U.S.-supplied equipment were seized by the Islamic Front.
The front is a coalition of Islamist fighters who at that time had broken with the moderate, U.S.-backed opposition. In a sign of how complicated the Syrian civil war is, the front has since joined the Free Syrian Army in the battle against al-Qaida.
The prospect of jihadists mingling with legitimate Syrian refugees headed for the United States apparently worries Obama administration officials.
That apparent stance in turn worries Rep. Adam Schiff, D-Calif.
"In terms of lending financial support [to the Syrian crisis], the response has been very positive. But in terms of providing actual refuge to refugees, we are falling dramatically short," Schiff told NBC News
Schiff and 72 other members of Congress sent a letter seven months ago to then-Homeland Security Secretary Janet Napolitano calling for refugee assistance.
In a recent response obtained by NBC, Brian de Vallance, Homeland Security's acting assistant secretary for legislative affairs, said the United States has begun "discussions" with the UNHCR and "other governments on expanded resettlement of particularly vulnerable Syrian refugees, such as victims of gender-based violence, torture and some medical cases."
De Vallance also said his department is "mindful that addressing such humanitarian needs must be coupled with robust security screening of refugee applicants."
Schiff told NBC Homeland Security talk of "discussions without action" means a "lack of decision."
He added, "They evidently don't want to say yes and they don't want to say no."