In additional to President Trump and Attorney General Sessions, there's someone else who believes it was unconstitutional the way President Obama enacted the Deferred Action for Childhood Arrivals executive order (or DACA):
Obama himself.
In November 2013, Obama delivered a speech on immigration in San Francisco, where a rowdy crowd repeatedly heckled him, demanding he legalize millions of illegal immigrants.
"Mr. Obama," someone from the audience shouted. "My family has been separated for 19 months now ... I’ve not seen my family. Our families are separated. I need your help. There are thousands of people — “
Obama, perturbed at the disturbance, unsuccessfully attempted to quiet the hecklers.
"Do you agree?" a heckler demanded, "that we need to pass comprehensive immigration reform at the same time we — you have a power to stop deportation for all undocumented immigrants in this country?"
Obama said the Constitution prevents him from doing so.
"Actually I don't, and that's why we're here," he replied. "I respect the passion of these young people because they feel deeply about the concerns for their families. Now, what you need to know, when I’m speaking as President of the United States and I come to this community, is that if, in fact, I could solve all these problems without passing laws in Congress, then I would do so."
"But we’re also a nation of laws," he continued. "That’s part of our tradition. And so the easy way out is to try to yell and pretend like I can do something by violating our laws. And what I’m proposing is the harder path, which is to use our democratic processes to achieve the same goal that you want to achieve. But it won’t be as easy as just shouting. It requires us lobbying and getting it done."