Bobby Outten, a county manager in the Outer Banks, delivered two pieces of bad news at a recent public meeting. Avon, a town with a few hundred full-time residents, desperately needed at least $11 million to stop its main road from washing away. And to help pay for it, Dare County wanted to increase Avon’s property taxes, in some cases by almost 50 percent.

Homeowners mostly agreed on the urgency of the first part. They were considerably less keen on the second.

People gave Mr. Outten their own ideas about who should pay to protect their town: the federal government. The state government. The rest of the county. Tourists. People who rent to tourists. The view for many seemed to be, anyone but them.

Mr. Outten kept responding with the same message: There’s nobody coming to the rescue. We have only ourselves.

“We’ve got to act now,” he said.

The risk to tiny Avon from climate change is particularly dire — it is, after all, located on a mere sandbar of an island chain, in a relentlessly rising Atlantic. But people in the town are facing a question that is starting to echo along the American coastline as seas rise and storms intensify. What price can be put on saving a town, a neighborhood, a home where generations have built their lives?

Communities large and small are reaching for different answers. Officials in MiamiTampaHoustonSan Francisco and elsewhere have borrowed money, raised taxes or increased water bills to help pay for efforts to shield their homes, schools and roads.

Along the Outer Banks — where tourist-friendly beaches are shrinking by more than 14 feet a year in some places, according to the North Carolina Division of Coastal Management — other towns have imposed tax increases similar to the one Avon is considering. On Monday, county officials will vote on whether or not Avon will join them.