"I want to say something very clearly, and this is going to be very disappointing to the people protesting the president and the people in Congress, like (Senate Democratic Leader Charles E.) Schumer, who have attacked the president for his lawful and necessary action: The president's powers here are beyond question," Miller said on Fox News.
Appearing also on ABC News, Miller said, "A district judge in Seattle cannot force the president of the United States to change our laws and our Constitution because of their own personal views. The president has the power ... to suspend the entry of aliens when it's in the national interest."
Miller said on CBS News that the judiciary was acting like "a supreme branch of government."
"One unelected judge in Seattle cannot make laws for the entire country," Miller told anchor John Dickerson. "I mean, this is just crazy, John. The idea that you're going to have a judge in Seattle say that a foreign national living in Libya has an effective right to enter the United States is beyond anything we've ever seen before."
Miller also suggested that the legal debate was not over the constitutionality of Trump's action, but rather over ideology.
"There is no constitutional right for a citizen in a foreign country, who has no status in America, to demand entry into our country," the adviser said on ABC.
"Such a right cannot exist. Such a right will never exist. This is an ideological disagreement between those who believe we should have borders and should have controls and those who believe there should be no borders and no controls."
Miller's exchanges with the Sunday show hosts were testy on other subjects as well. He punted when ABC anchor George Stephanopolous asked him about The Washington Post's report that retired Lt. Gen. Michael Flynn discussed the then-Obama administration's sanctions against Russia in conversations with that country's ambassador before Flynn was sworn in as White House national security adviser.
"I don't have any news to make you today on this point," Miller said, prompting Stephanopoulos to ask, "Then why are you coming in if you can't answer the questions being posed about the White House?"
On NBC, when anchor Chuck Todd asked Miller whether Trump still had confidence in Flynn, Miller said he did not know. Miller said his colleagues in the White House "did not give me anything to say."
"It's not for me to tell you what's in the president's mind," he told Todd. "That's a question for the president."
Miller also repeated the false claim that Trump underperformed in the general election because of "massive voter fraud." Miller provided no evidence to support his assertions in his ABC appearance - something Stephanopolous pointed out to viewers.
Miller repeated claims Trump made privately to senators this past week that he narrowly lost the general election in New Hampshire because thousands of Massachusetts residents were bused into New Hampshire to vote illegally there.
"I can tell you that this issue of busing voters into New Hampshire is widely known by anyone who's worked in New Hampshire politics," Miller said. "It's very real. It's very serious."
There is no known evidence of this happening.
Miller went on to say that there is "enormous evidence" of people being registered to vote in more than one state, of "dead people voting" and non citizens being registered to vote.
"George, it is a fact - and you will not deny it - that there are massive numbers of non citizens in this country who are registered to vote," Miller said. "That is a scandal. We should stop the presses. And, as a country, we should be aghast about the fact that you have people who have no right to vote in this country registered to vote, cancelling out the franchise of lawful citizens of this country."
At that, Stephanopolous intoned: "For the record, you have provided zero evidence that the president was the victim of massive voter fraud in New Hampshire. You provided zero evidence that the president's claim that he would have won the popular vote if 3 million to 5 million illegal immigrants hadn't voted - zero evidence for either one of those claims."
Miller's combative appearances pleased his boss, who apparently was watching from Mar-a-Lago, his private club in Palm Beach, Fla. Trump tweeted: "Congratulations Stephen Miller- on representing me this morning on the various Sunday morning shows. Great job!"