About six in 10 people, 59 percent, said the program is worth continuing, down from eight in 10 who said that in 1986 and 75 percent in early 2003.
The poll of 1,222 adults was conducted from July 29 to Aug. 2, and so respondents did not consider Wednesday's repair job on the shuttle. It has a margin of sampling error of plus or minus 3 percentage points.
The poll comes on the heels of an exciting outer space adventure completed Wednesday. A spacewalking astronaut gently pulled two potentially dangerous strips of protruding filler from Discovery's tile belly with his gloved hand, successfully completing an unprecedented emergency repair.
Astronaut Stephen Robinson, who is back on the shuttle Discovery, said both pieces came out easily during the spacewalk, which lasted just under six hours. He did not have to use a makeshift hacksaw put together in orbit that he brought along just in case.
"That came out very easily, probably even less force," Robinson said of the second piece. "I don't see any more gap filler. ... I'm doing my own inspection here. It is a very nice orbital belly."
NASA officials had determined that the exposed ceramic-fiber fillers could lead to overheating and a possible repeat of Columbia's disastrous re-entry.
CBS News Correspondent Mark Strassmann reports that for NASA, the repair was "picture-perfect."
"I was absolutely relieved," shuttle flight director Paul Hill told reporters. "I think you could hear the sigh of relief throughout the building over there. Anyone watching had to be impressed."
Although this was the first time an astronaut has ventured beneath the ship, CBS News Space Consultant Bill Harwood called the emergency repair job "a piece of cake."
"All the talk over the past couple days about this risky this how it's never been done before … well, it's never been done before, but he sure made it look easy," Harwood
Discovery, set to land Monday, is the first shuttle to return to orbit since the tragedy. So, Harwood says, NASA's doing all it can to ensure a safe landing.
"In the post-Columbia world, they're not taking any chances," he said.
New damage surveys developed in Columbia's aftermath detected the drooping material on Discovery.
As the spacewalkers returned to the airlock, the rest of the shuttle crew used Discovery's robotic arm and connected boom to inspect a thermal blanket below the commander's window that was ripped during launch, most likely by debris.
Mission Control told the astronauts that there was a "remote" possibility that the blanket might require a fourth spacewalk, and asked for their input.
There is some concern that the blanket — located right beneath the commander's cockpit window — might come off during re-entry and smack into the shuttle, Hill said. The blanket — a quilted fabric covering pillow-like stuffing — was ripped open most likely by launch debris and puffed up with air.