.... that won't work.
They dont work. There have been a handful of shutdowns longer than a day in the modern era. In none of them did the party trying to leverage the shutdown win the concessions they were seeking and, in each case, they also lost the public opinion battle.
Their opponents simply demanded a reopening of the government while pointing out all the ways the shutdown was hurting federal workers and American citizens. Eventually, the shutdown coalition cracked, the government reopened, they didnt win their policy major objectives, and they were worse off politically going forward.
It would unify the repugs, and make it harder to negotiate.
......congressional Republicans arent thrilled with Trumps actions.... Many of the backbenchers are worried about specific programs their constituents like being left to the whims of the administration. And the Senate Republican moderates are wary of the whole enterprise. If the Democrats shut down the government, they would immediately unite all of those dissenting Republican factions, by changing the question from Trumps excesses to the Democrats shutdown.
If not a shutdown, what should Democrats do?
Well, they could have standard negotiations in good faith, and then continue to call out Trumps impoundments or other spending moves. So long as the Senate Republicans are willing to do that as we stumble toward the eventual omnibus, its probably the least-worst option. Im not going to pretend it would be great, because the cloud of administration impoundments and other games would be looming over it, but it would likely proceed more or less as normal.
It sounds like doing nothing, but right now, doing nothing is probably the best strategy. Trump is unpopular, the midterms are rarely kind to the incumbent president, and in all likelihood, the Democrats are going to control the House and pick up seats in the Senate. Save the big fights for 2027, when they are on much firmer electoral, political and institutional footing.