The idea that Democrats benefit from a government shutdown over the Dreamers is absurd. Not only would Democrats have to explain that thousands upon thousands of federal workers are on leave because of a dispute over noncitizens. Democrats would also jeopardize the bipartisan goodwill the Dreamers enjoy by making them pawns in a cynical game. So unreasonable are the Democratic demands on immigration—more, more, always more, and with no changes to a rickety and leaky system—that one begins to wonder whether they actually want to settle the issue.
Perhaps the Dreamers and other illegal immigrants are more useful to the Democrats as tools of virtue signaling and electoral mobilization than they are as legal permanent residents in a country where the border is protected and laws are enforced. However, if my cynical interpretation is correct, then the Democratic strategy may backfire. I can think of one recent national campaign where immigration was central. It did not end in Democratic victory.