So for starters, just mathematically, your arguments don't necessarily hold up, or rather aren't mutually exclusive. "This person said he didn't support roughly half the people in this country, yet he got roughly half the vote". OK, so maybe the other half voted for him... There's nothing fundamentally "irrational" about the results per se. Also, it almost sounds like you're too young to have lived through other elections. This event clearly stands out in your mind as the political faux pas of the century or something, but I can assure you in every election most candidates say or do stupid things of this caliber and its par for the course for people to forgive them (What else are you going to do? Sacrifice your personal identity and vote for the other guy???).

Other things you're forgetting:

1. Only 62.3% of eligible voters even voted. So its not like half the country sided with him, its more like half of half (.47 * .623 = 29%). This also ignores all the people that disagreed with him that weren't eligible to vote, which is likely a LOT since it includes the undocumented and youth -- which theoretically fall into the category he doesn't care about. Right there alone you have a better explanation than "money".

2. Most people probably never even found out about Romney's comment, because they never find out about anything. You seem to be politically motivated and informed, you're making the mistake of assuming most other people are too.

3. You ignore that many people have deal-breaker issues and will give their guy a pass on literally everything else, ON BOTH SIDES. If I could somehow scientifically prove that a candidate would completely eliminate unemployment and poverty, he'd probably still lose a significant portion of the vote if he was overly pro-choice or pro-gay marriage. Same goes if he was pro-life or anti-gay marriage.

4. Both sides basically have half the media working for them spinning regardless of how much money they have. So in an environment where the media is constantly blowing out of proportion what "the other guy said" and going to absurd lengths to rationalize what "our guy said", it is not unexpected that the voting population becomes exhausted and skeptical about these events (this is a rational response btw).

5. People have their personal identities tied up in their political positions. Its not just this Romney comment, most times people prefer to defend their wrong positions than deal with the existential crisis that they were "wrong". This has way more to do with politics being treated as a team than as something external to yourself. You speak of a rational voting base? A rational voting base would have no party affiliation whatsoever, it makes no sense. You should be voting each time based on what is offered to you. Instead they see their party as their family. In the same way that if your dad said something unkosher you would take pains to understand what he "meant" while others would not, so too do people of a party try to rationalize what their candidate said vs what the other candidate said.

And so on. I'll reiterate that I'm making no comment on whether campaign finance is good or bad, just suggesting that Romney losing by "not enough" is just not a solid argument.