ROSEBURG, Ore. — Inside the big wood-paneled downtown library here, a sign spells out the future in four words. Come June 1, “All services will cease.”

For generations in America, small cities like this declared their optimism and civic purpose with grand libraries that rose above the clutter of daily life and commerce. But last fall, Douglas County residents voted down a ballot measure that would have added about $6 a month to the tax bill on a median-priced home and saved the libraries from a funding crisis. So this spring, it has been lights out, one by one, for the system’s 11 branches. The Roseburg central library here is the last to go.

“We pay enough taxes,” said Zach Holly, an auto repair worker in a shop a few blocks from the library who said his vote against the tax was not about libraries at all, but government waste. “I vote against taxes, across the board,” he said.

An instinctive reaction against higher taxes has been stitched into the fabric of America in recent decades, starting with the property tax revolts of the 1970s through the anti-tax orthodoxy expressed by many conservative members of Congress today. But few places in the nation are seeing the tangled implications of what that means — in real time — more vividly than in southwest Oregon, where a handful of rural counties are showing what happens when citizens push the logic of shrinking government to its extremes.