(a) The liberals generally dominate the Dem Party, but there are centrist who so far have been unsuccessful in taking the power away;
(b) The conservatives generally dominate the Rep Party, but there are centrist who so far have been unsuccessful in taking the power away;

2.  (a) Some libertarians abandon the Libertarian Party and join the Republicans to change the party

(b) Some Greens abandon the Green party and join the Democrats to change the party

3.  Or if they stay in the party, the Lib or the Green swing the results in close elections.

So there are different ways to influence the politics, but its much harder for the small parties in the USA than in Europe.  

Winner-takes-all system is prohibitive in that respect.

4.  There is also a problem of gerrymandering  which is another topic, but very important in the US politics. For example, in 2004, none of the seats in the California congressional (federal), and California State Senate and California State Assembly changed hands.  The Dems and the Rep got together in a backroom deal and designed their own safe districts, and each party gets elected in its own safe seat without any competition.  Sad. Travesty. Tragic. Comical.

Also note that despite the desire of some of us for a truly liberal Democratic party, the fact is that the Dems don't support a whole range of things that are supported by conservatives in other countries, like Canada. Stuff like single payer health, strong environmental policies (remember Kyoto was rejected 99:1 in the Senate), secular politics, etc., that are routine in Europe are not even under consideration here. America is simply not on the same page as Europe in many ways: What's the "center" here is off in the weeds in Europe, and vice versa.