His supporters let him down and let the country down when they spout this nonsense. It is precisely this attitude that led to a poorly prepared travel ban that will even fail in the Supreme Court because it denied due process to legal permanent residents.
According to Politico,
If there is a single issue where the president feels his aides have let him down, it was the controversial executive order on immigration. The president has complained to at least one person about "how his people didn't give him good advice" on rolling out the travel ban and that he should have waited to sign it instead of "rushing it like they wanted me to." Trump has also wondered why he didn’t have a legal team in place to defend it from challenges.He's absolutely right, for once. His inner circle actually kept numerous government agencies out of the loop.
A revised travel ban is his best option. Legally, he has nearly unfettered authority to deny refugee status. He went wrong when he attempted to interfere with the rights of legal permanent residents and others with lesser visa statuses. This can be corrected and will withstand judicial scrutiny.