Actually time is on the side of the Dems, which is why your suggestion will ultimately be forced on Trump. They simply WILL NOT give up on Chain Migration, as that is the only path for them to be remain a national party.
Eventually, Trump will be gone and they will either have a Republican idiot they can roll, or, more likely a Democrat eager to sign the bill that puts the final nail in this country. But for now, with nothing coming from DACA, they’ll just keep the millions of new, Third World, arrivals flowing in, unabated.
As to Trump, I don’t know what he ultimately thinks, but since nothing will change, Trump can at least make a credible claim that he tried to help the Dreamers, but was thwarted by the Dems.
If Trump plays his cards right, he can get enough allies elected in November to overrule the democrats, or get enough elected to change Republican leadership in Congress and use the simple majority rule. The democrats would be destroyed after 8 years.