How do modern politics and the political system impact the government's ability to serve its citizens?
The primary responsibility of a government is to provide for the safety and well-being of its citizens.
Different parties have different beliefs about how to accomplish those goals. The more unified and cooperative a political system is, the more it can accomplish. Sometimes, however, the political process gets in its own way, which can lead to problems for citizens.
We have seen several very good examples of this kind of political dysfunction in recent years with the budget struggles between the two chambers of congress and the president.
In 2015 Congress could not agree on a budget so the government had to shut down for awhile. In 2014 it also shut down when the Affordable Care Act led to conflicts that temporarily prevented passage of that year's budget. This has also happened in the deeper past—Ronald Reagan once vetoed a budget that didn't contain the tax cuts he wanted, leading to a shutdown in the 1980s. These shutdowns were not a disaster, but they did lead to the disruption of some services for some citizens. They occurred because the Republicans and Democrats could not reach an agreement without first pushing their debate as far as it could possibly go.
Most politicians and news analysts feel that these kinds of party showdowns happen more often these days. Supposedly the opposing parties used to be more cooperative in the interest of getting things done. With the fragmenting of voters' political allegiances has come a degree of political gridlock that makes it tough to get things done sometimes.
We also see problems with local governments when public employees, like sanitation workers or teachers, go on strike. This usually happens when the workers are dissatisfied with their pay or benefits. Sometimes it's the fault of whatever party is in power in that area at that time, but sometimes the workers' dissatisfaction builds up over time, and probably across administrations of both parties. The problem with the political process in this situation is how to balance the public's desire for low taxes with their employees' desire for good working conditions.
Sometimes government services do not appear to be equally distributed. In education, for example, school districts in poor areas generally have to make do with less—less money, fewer supplies, less qualified teachers, less motivated students. This is because much of education is funded through local property taxes, which are generated at a higher rate in affluent areas. While this aspect of the political system allows for local control of education, it also makes it more difficult for poorer areas to rise out of poverty. It is both an economic issue and a political one, since politicians could, if they chose, find a way to allocate funds equally.
In a democracy filled with diverse political groups, inequities and conflicts are going to arise. Parties want to solve these problems in different ways. These differences can, and often do, lead to inaction or marginally effective action by governments.