For those of you who don't know: Deferred Action for Childhood Arrivals (DACA), is a program which grants semi-legal status to illegal immigrants who came to the country as children. Congress tried to pass the DREAM Act granting a pathway to citizenship for these people several times, and each time it foundered. After several Republican supporters withdrew their support, Obama responded by creating DACA which allows these immigrants to get work permits though not permanent residency.
Obama later created a similar program: Deferred Action for Parents of Americans (DAPA), which would have granted legal status for parents of American citizens and green card holders. The media almost universally referred to this program, inaccurately, as a program which would have extended the protections of DACA to the parents of DREAMers. DAPA was challenged, overturned by the Fifth Circuit, and because of the death of Scalia affirmed by a deadlocked court. It's making its way back to the Supreme Court and with Gorsuch on the Court it will inevitably be overturned.
Trump promised to end DACA as well when he became president, and so far hasn't. I ran across this article, which purports to explain why, but it also gets wrong what DAPA was, and if you cannot get such a simple thing right I'm a bit skeptical of your competence as a journalist.
Still, the gist of the article is that Trump likes the DREAMers, and has therefore refused to end DACA. Since 80% of Republicans and 75% of Trump voters support DACA, it's also a smart political stance, which suggests it's unlikely to last. And to that end, several state Attorney Generals—likely with the collusion of the evil Keebler elf—have given him a deadline of 5 September: end DACA or we end it for you.
To me, it seems like DACA is on weaker legal footing than DAPA was, though for obvious reasons it's more politically popular. DAPA targeted a class of people who would be eligible for visas and green cards if they were in their own country; DACA carves out a new class for special protections. Since Kennedy tends to make decisions based on emotion, it's possible that DAPA will be overturned but DACA upheld, but I wouldn't bet on it.
As for the legality of DAPA, while it's obviously going to be overturned, my impression is that the president probably can grant stays of deportation to anyone he chooses, since he sets priorities for law enforcement, but it's not clear to me how he can grant work permits not authorized by Congress. However as I understand it the court's conservatives say he can do neither while the court's liberals say he can do both. I've asked avi in Discord to explain the liberal position, which I suspect will be more grounded in the law than the conservative one.
The point is that at this point, Trump has to choose between doing what his gut (and the polls) tell him is the right thing to do, and being seen as soft on immigration. No prizes for guessing which one I think he'll do, though he may surprise me. Trump apparently doesn't like being told what to do and may defend DACA out of sheer perversity.