There are many flavors of "socialists" in the US these days. Not all of them are actually socialists in the way most people would understand the term.
Sawant is from the Socialist Alternative Party, which is a militant group of Marxists/Trotskyists. Their ultimate goal is a new communist revolution in the US. She actually sounds tame compared to many other members of her party, but I suspect that is just because even she knows she can't spew all of her insanity out at once or people will realize what they voted for. The SA actually started as a group called Labor Militant and they were heavily involved in the WTO rioting in Seattle.
Sawant has no interest whatsoever in working within the system. Her only purpose is to disrupt and break the established political process. She would much prefer to see an angry mob take what they want by threat of force (or actual force) than to win it through the political process. This is because she (and her party) know that they can not get what they want by appealing to the majority because the majority of people will not see much personal benefit in what the SA is proposing.
This is all based on old revolutionary ideas from Russia where the workers class was convinced to revolt, and did so successfully, despite being a minority compared to other classes who would not benefit from the revolution. The idea was to then spread the revolution to rest of the world by way of solidarity with the larger working classes in other countries.
Most modern socialist groups in the US want to see a similar revolution take place here, but for some bizarre reason they think they can prevent the failures of other communist revolutions by somehow keeping the power-hungry, manipulative, dictators from moving in. Of course they fail before they start because their leaders lack the ability to look inward and see that they themselves are exactly those types of people. The leaders of these revolutions always establish themselves as dictators to ensure that the new revolution doesn't get corrupted by the ever present evil of capitalist forces. They then keep themselves (and their descendants) in power while claiming that they can't relinquish power because the revolution is still taking place.
Don't get me wrong, I also believe the political system here is broken to a certain extent, but as others have pointed out, communist revolutions have a well documented track record of producing far worse situations than the ones they replaced.
Unfortunately, groups that call themselves "socialists" have many decades of practice at drawing attention to themselves here in the US by being loud and obnoxious, despite being small in number. Now we are starting to see large numbers of people looking for alternatives to the political status-quo and the "socialists" have hit the ground running with their recruitment efforts while other alternative political groups are still trying to figure out how to get themselves heard.