But it wasn't a campaign issue for him when he ran for President in 1960
He visited Huntsville on Sept 11, 1962 (9-11-62, interesting date). About the closest thing to space I can find about his 1960 campaign was the "missile gap", which turned out to be fictious but he didn't know it at the time.
Now, it's possible LBJ mentioned space exploration in his 1964 campaign, most likely in Texas for bringing home the bacon. However, I can't confirm that one way or the other at the moment.