I don’t think politics is any more hopeless in the US than it was in 1800 (see: Jefferson’s underhanded campaigning). IMO the “hopeless” feeling that people get is this: almost every major policy, whether it be abortion, guns, environment, taxes, etc., will be opposed by roughly 40% of the population or more. That means that a lot of people are down on the direction of the government no matter what it’s doing. It’s the price we pay for plurality.
Everybody’s happy when the government is doing what they think is important and they (generally) don’t care what form it takes. When the government is doing something they don’t like, then it needs to be “fixed”.
Except that “40% of the population opposes everything!” problem only applies to problems where the citizenry is actually divided. There’s a whole host of issues where there is overwhelming consensus. The reason you never hear anything about these issues is because there’s consensus. The issues with consensus are settled issues, nobody argues about them.
I think you’ll have a hard time coming up with much of a list of topics that have a huge consensus. Even on topics that everybody thinks they agree on get muddy in the implementations. Take censorship, for example; you’d probably get a large majority who are against it. But conservatives don’t want smut on TV or in school libraries, and liberals don’t want commentators talking about how they’re afraid if Muslims.