Instead Atlantis has been sent back to its Florida launch pad to ride out Ernesto’s fury.
With the forecast improving Ernesto's winds no longer pose a serious threat to Atlantis.
NASA has been eager to fly Atlantis on the first International Space Station (ISS) construction mission since the 2003 Columbia tragedy.
The US space agenct has been aiming to launch the shuttle by September 7.
"We feel good about it," Leinbach told reporters. No official date has been set, he said.
Atlantis, standing on a massive mobile platform, was crawling toward its shelter when it was stopped five hours into a trek on a tree-flanked road and ordered back to the seaside launch facility.
The National Aeronautics and Space Administration has wanted to launch Atlantis by September 7 to avoid interfering with a Russian Soyuz mission.
Storm forecast
Ernesto is forecast to make landfall within the next few hours.
Contrary to expectations, it did not strengthen after leaving the Cuban coast, and its maximum sustained winds reached only 72 kilometres an hour at 2100 GMT.
The Miami-based National Hurricane Center expects the storm to sweep over the Florida Keys chain of islands and blow ashore in swampland southwest of Miami.
The storm could then travel along south Florida, head back out to sea and eventually come ashore again in South Carolina, possibly as a hurricane.
Experts initially feared Ernesto would hit Florida as a powerful hurricane packing the same intensity as Katrina, which killed 1,500 people after it slammed ashore near New Orleans, Louisiana, exactly one year ago.
Florida Governor Jeb Bush has declared a state of emergency and closed schools and several gas stations have run out of fuel as residents rush to fill up their cars in case they need to evacuate.