No, a lot of popular opinions on this site are just dumb as fuck. Go look up the number of people that play sports in high school or college and then look at the number of people in this country that actually are able to make it to the Pros. Again, those are lottery numbers. Getting a job at NASA or a comparable research institution is not as hard.
That's the problem. People like ya'll go around spreading this sentiment when it's not true. Ya'll must think that NASA only employs astronauts. It doesn't. Most people that work for NASA are not astronauts. They employ people in basically every discipline of the physical sciences, engineering, and mathematics. They have computer scientists and IT specialists and all types of technicians including jobs welders and electricians. On top of that, like all other government agencies and institutions they have a legal department, HR department, Finance department, and several other positions that aren't science related. So no, it's not harder to get a job at NASA than it is to get in the NFL, NBA, become a successful rapper.
But since ya'll like to paint it as me disagreeing just to disagree, maybe you'll like this answer from a PhD on Quora better.