In his speech, Cain praised President John F. Kennedy as a "great leader" for inspiring a national effort to put a man on the moon, a goal achieved when astronaut Neil Armstong stepped onto the moon's surface in 1969.I don't know what the reaction of the crowd was (the reporting wasn't that detailed) but I'd imagine it was friendly. You can usually get a warm response from a Republican crowd by coming out in favor of manned space exploration which is, when you think about, strange as hell.
"He didn't say, 'We might.' He didn't say, 'Let's take a poll,'" Cain said. "He said, 'We will.' And we did. Only for this president to move us back by canceling a major part of our space program."
Cain also criticized Obama for using Russian technology to ferry astronauts and cargo to the International Space Station.
"I can tell you that as president of the United States, we are not going to bum a ride to outer space with Russia," Cain said to loud applause. "We're going to regain our rightful place in terms of technology, space technology."
If you set out to genetically engineer a program that libertarians ought to object to, you'd probably come up with something like the manned space program. A massive government initiative, tremendously expensive, with no real role for individual initiative. Compared to infrastructure projects the benefits to business are limited. You could even argue that the government's presence in the field crowds out private development.
(Much has been made of the rise of private space firms, but barring a really big and unexpected technological advance, their role is going to be limited to either unmanned missions or human flights in low earth orbit for the foreseeable future.)
There have been efforts in libertarian-leaning organs (The Wall Street Journal, Reason, John Tierney's NYT columns) trying to argue that interplanetary exploration can be done on the cheap. These usually rely heavily on the blatant low-balling of Robert Zubrin* (Tierney, a science writer who has no grasp of science, made a particularly ripe mark), but even if we were to accept these numbers, it's still difficult to reconcile this kind of government program with libertarian values.
* On a related note, check out this other example of Zubrin's estimation skills.