There's a call on the United States to take in more of the refugees fleeing Syria's civil war, CBS News' Margaret Brennan reports.

President Obama bowed to international pressure and decided this week that the U.S. will take in around 10,000 refugees from war-torn Syria over the next year. The U.N. refugee agency says that number just isn't enough.

"The refugee crisis is not just a European problem; it's a world problem, and we have obligations," Mr. Obama said Friday.

Four million people have fled Syria, and now hundreds of thousands of them are flooding into Europe. Germany alone expects to take in 800,000 by year's end.

Reuters/Bernadett Szabo

"There is desperate need that's not being met," said David Miliband, who runs the International Rescue Committee.

He said the White House commitment falls short.

"The figure of 10,000 is deeply disappointing because it won't be adequate to the scale of the problem, which demands a global response on a far more effective scale," he said.

The policy change came after public outcry over the image of a 3-year-old Syrian refugee whose body recently washed up on Turkish shores.

Over the past four-and-a-half years of war, Syria's neighbors have shouldered much of the exodus.

During that same time, the U.S. accepted only 1,500 Syrians.

U.S. officials say the slow acceptance rate is due to intensive vetting, which can take two years or more to complete.

"The fact is, our main goal has to be to protect the United States," said Republican Congressman Peter King of New York.

He argues Americans' safety should be the primary concern.

"I know that ISIS will attempt to infiltrate those refugees and runs the risk of having terrorists coming into the country," he said.

The White House insists that no corners will be cut when it comes to security. U.S. officials have already selected the group of refugees who will come to the U.S. After they're processed, they'll be resettled in communities across the country starting sometime after Oct. 1.