I don't think Trump or the White House actually is the one making a real threat here, he spent the last few weeks making all these deals on this stuff or at least trying to make deals, he's caving some on DACA, on board for CHIP. The House has passed a bundle of things, including various continuing resolutions to punt past DACA.
It's McConnell trying to play a hand he doesn't have the votes for, with arguably Schumer doing the same thing in reverse. Only Schumer has the advantage of only needing 41 votes even though he seemingly doesn't want the position he's taking.
It's practically the same thing McConnell and Reid pulled with the names and numbers jumbled up. The White House and the House came to that temporary agreement and the Senate was like lol nope, and yet there seemed like there was a vote count for the Senators that would have passed it, and lots of anonymous sources pointed at the leaderships playing games.
Then the Senate always finds some bloc to go around leadership and ruin both their hands. Wasn't there a GANG OF SOME NUMBER in that instance? Lindsey Graham is apparently trying to form one. I can't remember how many times they've done these in regards to immigration that the leaderships have bottled up, which is why this is getting painted as DACA preserved for a hellscape anarchy vs. functioning beautiful great again government.