But soon after the press conference, Abbott's office released more details about the plan that struck a notably softer tone.

The governor's office clarified that the program is completely voluntary for migrants and would happen only after they had been processed and released by the Department of Homeland Security. And in addition to buses, Abbott also ordered the state to charter flights to transport migrants to the nation's capital. The migrants would have to show documentation that they had already been processed by DHS. Many immigration advocates have noted that providing transportation services for asylum-seekers to reach their final destination is something the state should invest in.

Abbott's announcement led to immediate criticism from both his left and his right. Immigration rights groups said his rhetoric was still dangerous.

"Any forcible busing of migrants across the country would be outrageous and blatantly unconstitutional," Kate Huddleston, a staff attorney at ACLU of Texas, said in a statement. "Given that Abbott cannot dictate where people are sent, he has already backpedaled on this heinous plan, announcing that it will be only voluntary."