The rating on corporate or government bonds is basically like your personal credit rating. For ordinary people, companies, and small governments, the credit or bond rating determines the interest rate they have to pay. That credit rating is the main source of information that investors use when deciding if they want to lend money.
However, the case of the US government is a bit different. People and institutions often invest in US treasuries as a kind of automatic action when they do not know what else to do. Even with the downgrade, US treasury bonds are the safest investment on the planet. Some large corporations may have slightly better credit ratings, but the market for their bonds is less liquid. That means it is harder to find someone who will buy them. You can literally sell off billions of dollars of US treasuries in a millisecond without really affecting the price you get for them. Financial institutions value that option.
The interest rate that people demand for holding US treasuries fluctuates all the time. It is not like a personal debt, where the rate gets fixed for years. The fluctuations in this interest rate depend more on overall economic conditions and world events than the actions of the government, but those actions do matter and people take them into account. The 'smart money' has already adjusted the interest rate based on the actions in Washington. The downgrade will not affect their decisions, because it gives them no new information.
The biggest affect of the downgrade will be on fuzzy things like 'consumer confidence' or 'business sentiment'. It will make people less likely to invest, which could hurt the economy. Nothing fundamental has really changed, but people are now more aware of the problems that exist.
One of the main problems with our economy is that there is not enough money. The inflation rate is way too low. The money supply in a country depends both on the central bank (the Fed) and the banks. After the financial crisis and credit crunch, the Fed printed a lot of money to make up for the change in bank lending, but it was not enough. We are in danger of a deflationary spiral, just like the Great Depression and Japan in the last two decades. Anyone who complains about inflation is completely out of touch, like a general fighting the last war.
The biggest problem with our political system is gerrymandering. That is the fundamental cause of the dysfunctional behavior. Politicians are not elected by the median voter anymore; they are elected by the median primary voter in a district designed to be full of people of a certain party. Political scientists have shown that congresscritters from the two political parties are getting more and more polarized over time. Their constituencies are actively rewarding them for this kind of ideological posturing, with the result that things start to fall apart.
Now for come practical advice:
The current situation of low returns on investment, lower economic activity, and high energy prices will probably continue for some time. This means that now is absolutely the best time to do things like improve the insulation in your house or get a more energy-efficient HVAC system. If you invest in these kinds of things, you will get a much higher return, in the form of energy savings, than you could get in a bank. Since the construction sector is still really depressed, you can probably get these things done pretty cheaply.
Getting an electric car is probably not practical now, but it will be in a few years. In the meantime, get a tuneup of your car to improve gas mileage.
In general, when shopping around for things, pay a lot more attention to total cost of ownership, of which energy efficiency is a big part. Paying an extra $200 for the washing machine with the best energy efficiency will earn you a far higher return than letting that $200 sit in the bank.
If you have any kind of medical problems relating to muscles or joints, think about things like buying really good shoes, or upgrading any tools you use frequently. You might find that getting a fancy ergonomic keyboard or high-quality garden tools will make your life better and dramatically reduce future medical costs. At a minimum, ask about tool sharpening at your local hardware store.
If you have any money sitting around the bank, you should seriously consider making these kinds of 'lifestyle investments'. It will be good for you and good for the economy.