A growing number of governors across the country are saying they will not allow thousands of refugees seeking sanctuary to relocate in their states in the wake of terror attacks in Paris.  None of the governors has the authority to prevent refugees from moving into a state, but many indicated they would not make it easy.

So far governors of at least 27 states have said they will not help harbor an estimated 10,000 Syrian refugees the Obama administration hopes to accept in the next few years.

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These states say they will not welcome the refugees:

On Tuesday:

Oregon Governor Kate Brown said her state would welcome Syrian refugees.

On Monday:

- California Governor Jerry Brown says refugees will be accepted in Californiabut he'll work closely with President Barack Obama to ensure any Syrian refugees coming to California are "fully vetted in a sophisticated and utterly reliable way."

- Gov. John Hickenlooper said Colorado will not join states saying they won't welcome Syrian refugees.

"We will work with the federal government and Homeland Security to ensure the national verification processes for refugees are as stringent as possible," he wrote in a statement. "We can protect our security and provide a place where the world's most vulnerable can rebuild their lives."

- Hawaii Governor David Ige said his state would welcome the refugees.

- Virginia Governor Terry McAuliffe said he won't try to stop Syrian refugees from entering his state.

- Pennsylvania Governor Tom Wolf said Syrian refugees would be accepted. Pittsburgh Mayor Bill Peduto is one of 17 mayors nationwide who accepted Obama's request to find a safe haven for families who fled Syria's war and violence.

- Oklahoma Governor Mary Fallin said the state would continue to accept refugees, but urged the Obama Administration to suspend the refugee acceptance program.

— Texas Gov. Greg Abbott ordered his state's refugee resettlement program not to accept any more Syrians, and some other Republican governors announced or suggested they were suspending cooperation with Washington on the program, at least until assured the newcomers were being vetted effectively for security risks. Among those governors were two other GOP presidential contenders, John Kasich of Ohio and Bobby Jindal of Louisiana. None of the governors, though, has the authority to prevent refugees from moving into a state.

—Republican lawmakers called for suspension of the federal Syrian refugee program and threatened to try to stop it in legislation that must pass by Dec. 11 to keep the government running. New House Speaker Paul Ryan neither endorsed nor ruled out that course.

—Republican presidential candidates, already skeptical if not hostile to the refugee-welcoming plan before the attacks, stepped up their rhetoric against it. Donald Trump said the U.S. should increase surveillance of mosques, consider closing any of them tied to radicals and be prepared to suspend some civil liberties. He'd been among the first to warn that the refugee crisis could represent a "Trojan horse" with terrorists infiltrating the ranks of innocent refugees. Calls by GOP rivals Ted Cruz and Jeb Bush to give preference to Christian refugees from Syria prompted a sharp rebuke from Obama. "Shameful," he said. "We don't have a religious test for our compassion."

At the heart of the debate is the Obama administration's decision to raise the nation's annual limit of 70,000 refugees by 10,000, with most of the new slots for Syrians, in the budget year that started Oct. 1.

That potential Syrian influx pales in comparison with the masses coming to Europe and those being accepted elsewhere. Canada, with just more than one-tenth of the U.S. population, plans to take in 25,000 Syrians in the next few months.

But indications that at least one of the attackers who killed 129 people in Paris may have crossed into France with refugees have given critics of Obama's plan a footing to demand a cutoff.

"Until we can sort out the bad guys, we must not be foolish," Republican presidential contender Ben Carson said after a Nevada campaign swing Monday. And he said of Syrians already in the U.S: "I would watch them very carefully."

Like Trump and others in the GOP race, Carson was critical of the resettlement program before Paris came under assault. But the attacks were persuasive to some who had been more open to the idea or on the fence.

"It's not that we don't want to, it's that we can't," Florida Sen. Marco Rubio said Sunday. In September, he'd been "open to that" if effective screening could be assured.

Bush, too, altered his tone, asserting the "focus ought to be on the Christians who have no place in Syria anymore," because "they're being beheaded, they're being executed by both sides." Before the attacks, he had spoken of moderate Muslims also being slaughtered in Syria, when arguing that the U.S. had a responsibility to protect them, as well.

The mood in Congress may be altering as well, although the issue was just taking shape. Ryan did not tip his hand on whether he would try to use House budget powers to counter an administration initiative that did not need congressional approval.

Republican Sen. Jeff Sessions of Alabama was among those suggesting such a tack. Absent congressional action, he said, "the United States will begin resettling tens of thousands of poorly vetted Syrian refugees who will eventually be able to bring in their relatives." Rep. Tom Price of Georgia, the House budget chairman, said the U.S. "must suspend our refugee program until certainty is brought to the vetting process."

Rep. Adam Schiff of California, senior Democrat on the Intelligence Committee, said security checks must be intensified, but "even with the most thorough precautions, there is some risk associated with allowing refugees into the country. And this is why the current crisis is a test of our character."

As in Texas, Louisiana and Ohio, Republican governors in Alabama and Arkansas spoke out against Syrian resettlement. Michigan Gov. Rick Snyder, who had earlier bucked many fellow Republican leaders by embracing the initiative, said he was suspending the welcome until federal officials reviewed security procedures and clearances. Michigan's "first priority is protecting the safety of our residents," he said.

The Associated Press contributed to this report.

Editor's Note: This story was updated at 3:00 p.m. Tuesday.