Everybody's disgusted to one degree or another with our government, and the answer most people bring up is, "More third party candidates!" But that's not really a good idea in our system of government, and here's an excellent article that explains why.
What about third-party candidates for Congress? Now, I hope you are familiar with our winner-take-all system which is mandatory in federal elections because of our Constitution. What this means is that you can win an election with a mere plurality of the votes, and that if you lose by even one vote you lose everything. And this has very real consequences. Suppose you have candidates from the Red, Blue, and Green parties. The Red candidate disagrees with you about abortion rights and the blue and the green candidates both represent your views on the issue nicely. Assuming this is a dealbreaker issue for you, in the sense that you won't support someone who disagrees with you, you can eliminate the red candidate and choose between blue and green based on some other considerations. If everyone behaves like you do, the blue and green candidates will split the abortion vote (for your position) between them while the Red candidate will get all the votes opposing your position. It's possible for the Red candidate to win with as much as one vote shy of two-thirds of the voters opposing their view on abortion. You can substitute for abortion any issue which sharply divides the Democratic and Republican parties, which increasingly means almost every social and economic issue under the Sun.
So, the first problem with third-party candidates is that they have to win or they risk being spoilers that throw the election to a candidate who holds views out of the mainstream for their district. A recent example of this occurred in Illinois' 8th District. Tea Party activist and deadbeat dad Joe Walsh won election by a margin of 291 votes. Green Party candidate Bill Scheurer won 6,494 votes. Democrat Melissa Bean was out of a job. The people of the 8th District were left with a moron to represent them.
Of course, once in a blue moon a third party candidate can actually win. This most often happens through the consent and conniving of one of the two major parties. For example, the Democrats simply agree not to field a candidate against Socialist Bernie Sanders of Vermont. Or, another example, the Republicans fielded a joke candidate against Joe Lieberman and Ned Lamont, and openly pulled for Lieberman's victory.