EUCHAREENA, Australia — Fleur Magick Dennis has stopped showering every day, allowed her vegetable patch to die and told her four sons to let the dishes pile up. Sometimes, all her family has is bottled water, and they have to preserve every drop.

A year and a half ago, the reservoir in their town, Euchareena, went dry, leaving the family and some other residents without running water.

“I didn’t think I’d be in this position, trying to fight for water for basic human needs in Australia,” Ms. Magick Dennis said.

As a crippling drought and mismanagement have left more than a dozen Australian towns and villages without a reliable source of water, the country is beginning to confront a question that strikes at its very identity: Is life in Australia’s vast interior compatible with the age of climate change?