They can now, and do. Presently they come across the border with Mexico via smugglers to avoid checkpoints. On the Canadian border it's much easier. Our immigration personnel have had their funding cut by Congress and they only hold them for 72 hours or so before releasing them after giving them a hearing date. Surprisingly to the government, they don't show up for their hearings. They just disappeared from sight.
The government has reported some 4,000 such detention cases involving "visitors" from suspected Middle East terrorist nations. The government suggests the numbers may be closer to 12,000. Often it helps to just step back, look at government, and wonder what they're thinking.
I note, too, that we've had the GATT since 1947, and, amazingly, we still have sovereignty and a congress and a president and everything! It's amazing!