"It seems that a lot of the chaos yesterday could have been avoided, had you at least included some sort of timed grace period," Chuck Todd asked Priebus on NBC News' "Meet the Press." "Why was that not included?"
"Well, I don't think you want to have a grace period," Priebus replied. "Then people that want to do bad things to Americans will just move up their travel date two days in order to get into the country before the grace period's over."
Priebus said that "a lot of people," including U.S. Customs and Border Protection, "would just tell you you've got to rip off the band-aid."
"It wasn't chaos," he insisted. "I mean, the fact of the matter is 325,000 people from foreign countries came into the United States yesterday and 109 people were detained for further questioning. Most of those people were moved out."
Priebus said that a "couple dozen" people are still being detained.
"I would suspect as long as they're not awful people, that they will move through before another half a day today, and perhaps some of these people should be detained further," he said. "And if they're folks that shouldn't be in this country, they're going to be detained. And so, apologize for nothing here."
Following Trump's signing of the order, massive protests broke out at airports around the United States.
Watch their exchange below: