How would the United States exist without a government?

Much like Sudan and Somalia exist/existed without governments. 

It would be 10, 000 warlord hell holes. The people would flee to other countries in large numbers.

No nation exists without a govt.

Most people will therefore readily accept the notion that certain institutions have a legitimate right to exercise authority and to make decisions for the common good. With no government to make decisions for the community, every individual would be left to follow the dictates of his own conscience. Would this promote unity? Probably it is more likely that each individual would tend to pursue his own interests, often to the detriment of the equally legitimate rights of others. 

They managed to exist through the time Trump was in office but only just.

it would not.  by definition, the "United" States is the republic made up of the collection of our States

No body is calling for that . We the People need to tame the Frankenstein creature living in the DC marsh, before it cancels We the People permanently .

It would be a lot of small independent countries between two big countries.

It hasn't been tried.

Without government, you would have no states. Ergo, no United States.