A lot of the reason for the gridlock (and the rise of things like the arch-conservative Tea Party and religious right) has to do with the present system of government giving too much voice to sparsely populated rural states. There were reasons this was done back when the republic was founded to prevent more populous areas from overriding the concerns of farmers, who at the time constituted a much larger share of the population than now. Times have changed. Now with 2 senators per state regardless of population the concerns of urban areas often aren't being heard. NYC for example sends far more money to Washington and upstate than it gets back in spending. The subway system has been systematically defunded over the last four decades even though it's relevant in some way to probably 4% or more of the US population. And in general the US lags the rest of the world in local rail transit, high-speed rail, bike infrastructure, walking infrastructure, etc. These are valid concerns which are costing us economically. However, they're also unlikely ever to be addressed when people in states where only cars and highways matter have a disproportionate voice. We probably need to just go with one legislative body with representation proportional to population. I also think we should give the President some powers to cut programs, perhaps limiting this power to no more than a certain percent of GDP. The rationale for this is much government spending is sacred cows which often do little for us on any level, but which have been perpetuated for decades due to lobbyists. Farm subsidies come to mind, as does bloated defense spending. Do we really need to spend as much as the 7 other top nations combined on our military? Power to cut some amount of the budget each year, with no recourse for Congress to restore it, is a power needed by the President. A lame duck President especially can trim lots of unnecessary programs without worrying about political fallout.We'd probably be a lot saner as a country if we adopted a Parliamentary Government and found some new ways to derive the basis for our representation. But really, nothing is going to change except that the middle ground is going to become smaller and harder to find. I don't think we have the will to truly do anything about it.
The tax system needs to change as well. It's becoming increasingly harder to track income or decide what types should or shouldn't be taxed. There's a good reason the founding fathers disallowed an income tax in the constitution. We need to repeal the 16th Amendment and get rid of income and payroll taxes at federal, state, and local levels. Accountant lobbies have fought against this, but in the long run this will make us much more competitive.
I'd also like to see most legislation on all levels of government have expiration dates. All too often we keep laws on the books which serve no useful purpose. It may not matter if they're never enforced but often they are just to harass some segment of the population.