What was the significance of Thoreau's comparing the nation's "establishment" with the "households" of its citizens?

Thoreau wanted to show that a household does not need to be an establishment full of wealth and furniture, as households simply exist, without the need for luxury.

Although you have not shown the text that your question refers to, we can see from the context of your question that you are referring to "Walden" written by Thoreau.

This book was written when Thoreau was living alone in the desert, where he reflected on many points of society. In this book, we can find concepts such as:

Thoreau's thoughts manage to fit into our society and even with all modernity, we can see that he had a very punctual reading about humanity and our relationship with wealth and with the individuals around us.

You can find more information about Thoreau at the link below:

president franklin roosevelt supported the tva as part of his first new deal measures approved by congress in 1933. this new agency was designed to control floods, produce electric power, and improve the lives of people living in the tennessee valley. the tva accomplished many of these goals despite problems.