Two Very Different Concepts of Impossible

Which of these positions makes more sense?

When it comes to securing the border, liberals and Democrats claim building the wall is impossible. People have been building walls for 1000s of years.

When it comes to allowing 10,000+ Syrian refugees to come to the United States, conservatives and Republicans claim it is impossible to properly vet these people who have no passports or no documentation from a country with a heavy terrorist presence and a hostile government.

To my mind, masonry construction, regardless of the scope of the project, seems less daunting than modern intelligence and counterterrorism work.