TUBMANBURG, Liberia—American and Liberian soldiers hammer, saw and sweat in the afternoon sun here in a frenetic campaign to build the county’s first Ebola-treatment unit. Soon, the soldiers will have floodlights to work round-the-clock shifts.

The unfolding epidemic has killed more than 4,400 people, mostly in West Africa. Everything in Liberia was needed weeks ago, and the Ebola-treatment centers are no exception. A month ago, President Barack Obamavowed to build 17 units. Soldiers have yet to complete one. (Further reading: Obama to name Ron Klain as Ebola czar.)

“My team has one speed, and that’s flat-out,” said Bill Berger, the leader of the U.S. government’s Ebola disaster-response team for West Africa.

Liberia’s health infrastructure was barely able to respond to the needs of its people before the outbreak. Ebola has since steamrolled it. As a result, the U.S. and other countries are essentially creating a health system from scratch on extreme deadlines.

The challenges are huge: Power outages and a lack of basic medical supplies are among them. Decrepit roads and heavy rains plague construction sites. Doctors and nurses were already in short supply because of years of low pay.