The response to Sputnik was slow, and was mostly things like the National Defense Education Act of 1958.
The space race was not necessary, but was based on part fear and part jingoism (the two are never far apart). Otherwise, not much pushed us to the Moon. At lot of people thought the attempt to go to the Moon was "stupid" and that instead of even unmanned missions it was better to money to be spent at home. In the "guns or butter" tussle, NASA was still "guns".
If Nixon had won in '60 and proposed it, I suspect the (D) Congress would never have funded it. As it was, by '66 NASA funding was bitterly fought by other interests who said we needed the money to be put elsewhere. It was largely curtailed after it could be claimed we'd made our point and learned all we could from a dangerous program. Oh, yeah, and we needed to put the money elsewhere, but that was presented almost as an afterthought.
I was a big adherent of the manned Moon missions. Nobody hardly cares about unmanned probes. There's no PR in it, apart from pretty pictures. Let's face it, the pictures from Mars ... Not so pretty. From the Moon? Dismal. Let's not even discuss the Soviet Venera pictures. Cassini had some nice eye candy, of course. But not one of my students knew who Cassini was; they assumed Cassini was the designer (most thought Hubble was named after somebody still alive who designed or pushed for the Hubble. "What? He's DEAD?!!"
Without PR, you have trouble getting funding. Hubble pictures? Oooh, let's have mission to repair it, extend its life. Spitzer? Webb? Chandra? No pretty pictures. Even ALMA ...
Make the Mars mission about the people involved in it, those going on the mission, the risks and dangerous, and sure, people will split. It's a soap opera, and even the highly educated tend to like soap operas; hell, just look at how American politics is presented. But people are split already, but it's pretty much 99% uninterested and 1% interested. The new split will be much closer to 50-50%, and might actually get even those uninterested in the science thinking, "This could be cool." Even a 40-25-35% split would be a breakthrough. Musk's wanting to die on Mars created more of a stir than the Mars probes' all self-assembling into a Madonna robot and doing the hoochie-koochie would have.
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