So far, the Tea Party is not a tradiditional American political party. It does not have ballot access like the Republicans and Democrats have, and it does not run candidates. The best description of the Tea Party is an effective political pressure group. This may change, but as of right now, that's how it is.
The Tea Party is most concerned about taxes and spending. Specifically the US budget is un sustainable, we cannot borrow 40% of Federal spending for ever, there isn't that much money in the world. In fact the only reason the US can still sell Treasury bonds is that investors don't think the US will default on them, and all the other places to invest (stock market!) look worse. As soon as Great Depression 2.0 clears up, treasuries will compete with other investments at a disadvantage. The Tea Party was created to oppose this flushing of the American dollar and economy down the drain. I receive constant emails urging the Tea Party members to stick to their guns, (taxes and spending) and avoid wedge issues like gay marriage and abortion.