Most U.S. governors have made clear they don’t want Syrian refugees in their states after the deadly Paris terror attacks, but only Congress appears to have the authority to stop President Obama’s plan. 

And Capitol Hill lawmakers are moving swiftly. 

Senate Majority Leader Mitch McConnell, R-Ky., and House Speaker Paul Ryan on Tuesday both called for a “pause” in the administration’s refugee plan, which includes resettling 10,000 Syrian civil war refugees through 2016.

“Right in front of us is a refugee situation that requires a pause,” Ryan, R-Wis., said on Capitol Hill. “Our nation has always been welcoming, but we cannot let terrorists take advantage. ... This is about national security.” 

He gave no specific details but said a task force is working on legislation, adding: "It's better to be safe than to be sorry." 

A total of 30 governors, including one Democrat, so far have expressed opposition to the plan in the wake of Friday's attacks, executed by at least one suspected Syrian refugee with ties to the Islamic State terror group and who perhaps slipped through Europe’s vetting process.

However, scholars and legal experts acknowledge that governors have little if any power to stop refugees from entering their states, citing the Refugee Act of 1980 which gives the federal government the authority. 

“Immigration is a federal responsibility,” James Carafano, a national security and foreign policy analyst with the Heritage Foundation in Washington, D.C., said Tuesday. “States cannot say, ‘You cannot come into this country.’ But they can say that they’re not going to part with state resources. They can do that.”

The White House said late Tuesday that Chief of Staff Denis McDonough hosted a call with 34 governors that included an "extensive" question and answer session among administration officials. Of the 34 governors on the call, 13 asked questions, according to the White House.

Administration officials also reiterated that President Obama's top priority is "the safety of the American people."

"Even as the United States accepts more refugees-including Syrians-we do so only after they undergo the most rigorous screening and security vetting of any category of traveler to the United States," the White House said.

Ryan’s announcement followed a flurry of similar proposals from Republican senators, including at least two presidential candidates, following the Paris attacks in which 129 people were killed and hundreds of others were injured.  

On Monday, Alabama Sen. Jeff Sessions called on Senate appropriators to cancel the "blank check" for overall U.S. refugee-resettlement efforts that would be included in a bill to fund the federal government after Dec. 11.

Sessions argues the overall plan calls for resettling at least 85,000 more refugees worldwide and “an unlimited amount of money to be spent on lifetime welfare and benefits … without a penny of offsets.”

He cited a Heritage Foundation study that forecast the total cost of resettling 10,000 Syrian refugees at roughly $6.5 billion. Sessions was joined Tuesday by Sen. Richard Shelby, R-Ala., in calling for a provision in the "omnibus" spending bill to block the funding unless and until Congress votes separately to authorize it and offset its costs. 

Texas Sen. Ted Cruz, a presidential candidate, in September expressed his concern about the Syrian refugee program. In a letter to top administration officials, he questioned whether the refugees were being properly vetted for ties to the Islamic State, Al Qaeda and other radical Islamic groups.

On Monday, Cruz promised legislation to keep Muslim Syrian refugees out of the United States.

He told CNN that President Obama and Democratic presidential candidate Hillary Clinton’s plan bring them into this country after what happened in Paris “is nothing short of lunacy.”

More than 2,000 Syrian refugees have been admitted to the U.S. already since the start of the Syrian civil war in 2011. 

Kentucky GOP Sen. Rand Paul, another of the Senate’s GOP White House candidates, on Monday also announced legislation that would suspend issuing visas in countries “with a high risk of terrorism” and impose a waiting period for background checks on visas being issued in other countries until Americans can be assured terrorists cannot enter the country through the U.S. immigration and visa system.

“The time has come to stop terrorists from walking in our front door,” said Paul, who first drafted the legislation in the wake of the 2013 Boston Marathon bombings, committed by two refugees.

Ryan’s announcement also came just hours after former Republican House Speaker Newt Gingrich told WMAL Radio that Congress should try to block the Obama refugee plan by withholding federal funding in the so-called “continuing resolution” next month.

Iowa GOP Sen. Chuck Grassley, chairman of the Senate Judiciary Committee, already has been trying to include a rider in the spending resolution that would keep Obama from using taxpayer money to resettle Syrian refugees until the U.S. intelligence community approves the program.