There are many effective ways for the Green party to become a force in this country without that dramatic, suicidal charge up Capitol Hill. Why you can't beat the house Politicians can forget their promises and get by with it because FEC election law makes campaigns legally independent of the parties they run on. They raise their own money and run their own campaigns, and in most states get on the ballot in voter primaries instead of party conventions. That, plus the fact that parties have no legal control over their candidates in Congress, makes it impossible for any party to control the Congressional agenda, even if its candidates have the majority in Congress. But obviously you don't even get a majority in Congress without winning in a majority of Congressional districts across the country, and Greens have yet to win a single district in the last ten years.
Third parties overlook the power in state legislatures.
The state party in power redraws Congressional district lines every ten years based on the Census. They also control federal ballot access and the way presidential electors are allocated. Ballot access laws were rigged to kill the Populist movement. An even higher barrier is the Constitution itself. The built in barriers to drastic changes in our system of government were detailed by Professor Howard Zinn in his People's History of The United States .