Some groundwork: why do we have governments? To allow us to live in peace with people we've never met before, who we could otherwise kill, rape, and steal from, without consequences. It's a giant machine to enforce the golden rule, "treat others how you'd like to be treated". Of course, governments do a lot of extra things, but they're just that, extra.
The socio-political landscape has changed a lot since the 1700's. I think the biggest difference now is that nations are much less homogeneous than they used to be. In america in the 1700's there was a dominant faith that provided a set of common standards, e.g. that murder, homosexuality, and theft were all wrong. This is no longer the case, and people have become polarized around many different issues. Technology allows us to become convinced of the rightness of our own cause, through association with like-minded individuals.
Another significant change is that people are much more likely to move around the country, and have friends and family in different states and countries. Using geography as the basis for government divisions (counties, states, nations) is still a good idea, but is becoming less and less so every day.
The conventional solution to the first problem is to give more legislative power to the states, so that, for example, people in the bible belt can have more conservative laws and people in California can legalize pot. This isn't a long term solution any more, because of the second problem.
So we have widely-differing views on what should and shouldn't be legal, but we can't just tailor certain laws to certain geographical areas.
Given these factors, I make the following recommendations:
* Remove the states, and combine the Senate and House of Representatives into one. Allow cities and counties to control any and all issues that are linked to specific locations.
* Stop legislating morality. Enforcing the Truth (by any definition) isn't part of the government's core purpose. I personally believe that abortion is murder (although in a certain subset of cases it is justified), but this is an issue that comes down to personal conviction. It is therefore out of scope for the government. Theft, on the other hand, should remain illegal because it is demonstratively bad for social stability.
* All laws should be subject to rigorous logical and scientific analysis. For example, if a particular trade policy cannot be proven to have a net positive impact on the happiness of people, it should not pass.
* This would involve setting up a fourth branch of government, which is responsible for collating and evaluating scientific data, and performing the analysis of proposed laws. This branch, like the judicial branch, would have the power to veto laws. I envision that for every law, a formal scientific proof will be made available to the public. This will provide a degree of public accountability.
We now have a system in which bad laws (hopefully) won't get passed the scientific analysis, so the negative impacts of populism (rule by the popular) is decreased. Now, notice that the format of congress was decided when we didn't have instant communication. Therefore:
* Take away the congressmen, and make parties (rather than people) the fundamental unit. Discussions between parties should take place online, or at least be aggregated online. Copies of the discussions should also be made available at all public libraries.
* Allow people to choose a party to represent them, or create their own. Parties will have voting power proportional to their number of supporters (measured in votes, not verbal declarations), and a party must have more than 0.5% of the votes before it gets into congress.
* Parties must have a declared high-level policy on every issue, and they will be bound by these policies. This is to prevent people from setting up specific-issue parties; people must learn to support a governance paradigm that is bigger than any specific issue. Note that this does not stop parties from negotiating about details.
* Elections at the moment are a sham, so instead have rolling elections. After a person votes for a party, they cannot change their vote for 3 months + (some random number less than 14) days. Note that the random number is different to each person, and changes each time the person changes their vote. Within a few years every day will be equally an election day. The purpose of letting people only vote every 3 months is, again, so that people realize that governance is bigger than their one pet issue.
* Any party in congress can propose a law, as can any group of citizens larger than 1% of the population. It passes into law when it (or a later revision) has the support of 50% of the votes in congress, as well as the support of the fourth branch of government.
Finally, because we're a global community now, no law will be passed if it steps on the rights of people from other countries, as given in a extended Universal Declaration of Rights. Declarations of war will have to be proven to be beneficial to everyone in the world, not just citizens of the USA. This should hopefully prevent another Vietnam or Iraq.