SAN ANTONIO -- Eight Syrian refugees turned themselves in to immigration authorities along the U.S.-Mexico border this week, officials said Thursday, and their chances of being allowed to stay are unclear due to political upheaval in the wake of the Paris attacks.

Two families -- two men, two women and four children -- presented themselves Tuesday at the point of entry of the west Texas city of Laredo, the Department of Homeland Security said in a release. The men were taken to a U.S. Immigration and Customs Enforcement detention centre in Pearsall, and the women and children to one in Dilley.

Republican Gov. Greg Abbott, who along with several other governors across the country recently ordered state officials to suspend entrance for Syrian refugees following last week's deadly attacks in Paris, tweeted a link Wednesday night to the conservative Breitbart News Network website, which reported that Syrians had been "caught" at the border.

"THIS is why Texas is vigilant about Syrian refugees," the governor wrote.

Republican presidential candidate Donald Trump followed suit Thursday with a tweet of his own: "ISIS, Maybe? I told you so. WE NEED A BIG & BEAUTIFUL WALL."

Hundreds of thousands of people have fled Syria to escape the civil war, most of them to Europe. For Syrians with means, a lengthy trek to the U.S. border could provide another path to asylum. And the recent arrivals appear to stand a reasonable chance of staying in the country, at least for a little while.

Between 2004 and 2013, some 1,449 Syrians were granted asylum in the United States, most in 2012 and 2013, and were not part of the 70,000 refugees from around the world that the U.S. accepts annually. Only 9 Syrians were deported in 2014.

The Obama administration announced earlier this year that the number of people invited to move to the U.S. as refugees would be increased to 85,000 in the coming year, including about 10,000 Syrians. That program is now under scrutiny, and the U.S. House overwhelmingly approved Republican-backed legislation on Thursday that puts up new hurdles for Syrian and Iraqi refugees trying to come to the U.S.

For years, people have attempted to cross into the United States by way of the Mexican border. More than 145,000 people from countries other than Mexico were apprehended at the U.S.-Mexico border during the 2015 budget year that ended Sept. 30, though the overwhelming majority was from Central America.

Making the trip from a place like Syria can be both costly and difficult, but immigrants from countries other than Mexico or Canada cannot be quickly repatriated and are often detained for at least a few days after crossing. Plus, asylum seekers who pass the initial credible fear interview, the first step in the asylum process, are often released from custody to await a court hearing. Currently, a backlog of more than 450,000 cases is pending in federal immigration courts.