Updated

Key Republicans and Democrats in the Senate indicated that more support is building to either "pause" President Obama's plan to resettle Syrian refugees in the United States, or to at least learn more about that plan in a classified setting.

Senate Majority Leader Mitch McConnell, R-Ky., told reporters the government is not able to adequately vet refugees and prevent terrorists from entering the country, and that he wants a delay.

"At the very least it strikes me that we need a pause or a moratorium because the American people are quite concerned and upset at the possibility of terrorists coming into this country through some kind of refugee program," McConnell said.

Minority Leader Harry Reid, D-Nev., stopped short of calling for a halt to the resettlement program, but left open the door to suspending the initiative, and said he wants to hear more about the specifics of the plan in a classified briefing.

Reid said he has already spoken to the Obama administration about bolstering the vetting process for refugees entering the United States."The White House has indicated to me they are looking at this," Reid said, adding, "Congress has an important role to play."

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