A successful democracy is one where people vote and their vote has meaning. In 2008's presidential election, the US voter turnout was about 57%, the highest in 40 years yet much lower than most other democracies in wealthy countries. The fact that Americans don't vote is the number 1 symptom that America's democracy is struggling.
Australia, with its 95% voter turnout, has solved the question of how to get people to vote by making it the law. Yes, you must vote in Australia though about 5% of enrolled voters still skip this obligation resulting in a small fine. Failure to pay the fine can trigger a court hearing.
I am certain that some Americans reading this statement will think, "Choosing to not vote is an expression of my freedom of speech." I'll let the constitutional scholars debate that question knowing that this argument is little more than intellectualized apathy or laziness. Apathy stems from believing that elections aren't important or that their vote won't have any impact. Apathy needs to be addressed in other ways, but requiring people to vote would certainly change the dynamic of politics in America.
The main positive of requiring the vote would be that the government would reflect the voices of the vast majority of Americans rather than skipping the opinion of over 40% of the population. The main negative is that many of those who would now vote solely due to legal obligation will either make uninformed choices or that alternative candidate Mickey Mouse might get elected.
When I teach, some shy students complain that class participation is part of the final grade. I tell them that the rest of the class might benefit from hearing their ideas, but that we don't read minds.
As for compulsory voting in Australia, it has existed for over 80 years without any serious attempt to eliminate it. Maybe that's a good enough reason to give it some consideration here, in the land of over 40% voter no show.