The question has been framed in the streets: is a government that impoverishes healthcare and nutrition, flouts the law, enriches its officials, imprisons babies, and kills its citizens worth the money it collects, much less the respect and obedience it demands?
Democrats have nothing to lose by shutting down the government to force the majority party to respond to these questions and the one that looms over all: what, if any, is the political and moral future of the US?
Personally, I think that a future incarnation of the United States can be one nation, but divided into four regions, each with their own president and branches. Western, Middle, Eastern, and Outer America. The outer region is places outside of the contiguous US, such as Alaska, Hawaii, Puerto Rico, military bases like Djibouti, Greenland, and so forth.
These presidents can elect a Figurehead President, who heads the national executive for one term, and no more. Each region donates soldiers and other resources to the national government, and the national court is expanded to have an equal number of justices from each region. I am thinking about 21 justices - 4 from each region, and each president selecting a justice who represents their executive branch during the tenure of their president.
This would make it much harder for any one faction to have controlling power over politics, and make genuine collaboration much more likely.