Donald Trump appears determined to send migrants arrested at the southern border to “sanctuary cities” around the US, a scheme meant to exact revenge on his Democratic foes, despite fierce political opposition and doubts over the legality of such a move.

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On Saturday night, to widespread consternation, the president tweeted that it was: “Just out: the USA has the absolute legal right to have apprehended illegal immigrants transferred to sanctuary cities. We hereby demand that they be taken care of at the highest level, especially by the state of California, which is well known or [sic] its poor management & high taxes!”

On Sunday the House homeland security chair, Bennie Thompson, and judiciary chair, Jerrold Nadler, both dismissed the claim.

“[Trump] has no right to spend money appropriated by Congress for other circumstances,” the New York Democrat told CNN’s State of the Union. “[He should not] use immigrants or people who are claiming asylum as pawns in a fight with political opponents … it’s another misuse of presidential power against the law.”

Nadler also said he had “heard from whistleblowers” that Trump’s adviser Stephen Miller was the author of the sanctuary cities idea and should appear before Congress to explain it, as he “appears to be the boss of everyone on immigration”.

The president likes the idea and Democrats have said they want these individuals into their communities Sarah Sanders

Should Miller claim executive privilege to avoid such an appearance, Nadler said, that would be inappropriate as he “seems to be making the decisions, not the cabinet secretaries who come and go”.

Trump has grown frustrated over the situation at the border, where tens of thousands of migrant families are crossing each month, many to claim asylum. He recently shook up the top ranks of the Department of Homeland Security (DHS), forcing the resignation of the secretary, Kirstjen Nielsen.

On Sunday Rick Scott of Florida, a Republican member of the Senate homeland security committee, told CNN he did not know if the sanctuary cities plan was “legal or illegal”, but added that such cities “are illegal” and show “clear contempt for the law”.

Cities with sanctuary policies generally prohibit cooperation with federal immigration police. More than 100 local governments have adopted such polices.

The White House press secretary, Sarah Sanders, told ABC’s This Week the sanctuary cities plan was “not the ideal solution”.

“The president heard the idea, he likes it,” she said, perhaps suggesting Miller was indeed its author, before adding that it was among several options. “The president likes the idea and Democrats have said they want these individuals into their communities so let’s see if it works and everybody gets a win out of it.”

She said Democrats should work with the president on immigration reform. Scott agreed, saying: “Why don’t we try to solve the problem? We don’t want illegal immigration, we want legal immigration. I’m from a state that loves immigrants.”

Scott also said Trump could simply be “just saying this to make everybody crazy, make everybody talk about it on their shows”. He also joined Nadler in flatly stating that if true, Trump’s reported offer to pardon the acting homeland security secretary, Kevin McAleenan, if he ignored the law was wrong.

New research, meanwhile, said that if the administration does attempt to send migrants to sanctuary cities, it would make it easier for them to stay in the US.

According to a team from Syracuse University in New York, such a move would put thousands of migrants in cities welcoming to them and more likely to rebuff federal deportation orders. Furthermore, many such locations have more resources to help migrants make their cases to stay in the US than smaller cities. Some of the nation’s biggest immigration advocacy groups are based in San Francisco, New York City and Chicago. The downside for the migrants would be a high cost of living.

The Transactional Records Access Clearinghouse at Syracuse found that migrants in cities such as New York and Los Angeles are 20% less likely to be arrested than in cities without sanctuary policies.

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George Gascon, district attorney for San Francisco, told the Associated Press: “With immigrants being less likely to commit crimes than the US-born population, and with sanctuary jurisdictions being safer and more productive than non-sanctuary jurisdictions, the data damns this proposal as a politically motivated stunt that seeks to play politics with people’s lives.”

Shipping migrants to Democratic strongholds would also raise financial, logistical and legal issues. The transportation of migrants would be costly at a time when Immigration and Customs Enforcement (Ice) is stretched, having released more than 125,000 migrants pending court dates since 21 December, mainly in border states.

Flights chartered by Ice cost about $7,785 per flight hour, according to the agency, and require staffers including a medical professional. The agency also uses commercial flights. Longer transports would increase liability, especially considering that many in Ice care are families with young children.

The administration actually has plenty of space to detain families. As of 11 April, the nation’s three facilities to detain migrant families were nowhere near capacity, including a Pennsylvania facility housing only nine people.

It is also unclear how long the migrants would stay in sanctuary cities, because under current law they are required to provide an address to federal authorities, typically of a family member, as a condition for their release.

“It’s illogical,” Angela Chan, policy director and senior attorney with the San Francisco-based Asian Law Caucus, told the AP. “It’s just alarming that they are spending so much effort and so much time to engage in political theater.”