The Tea Party's economic view is that cutting government (with the exception of the military... of course), will solve the USA's economic woes. Unions are in a position to demand raises and benefits that would be required to be provided by the government. So naturally, if you remove unions, you remove that element of spending in our government... according to the Tea Party.
The simpler explanation is that unions are on the opposite side of the political spectrum to the Tea Party. So they must be destroyed!! But, that the spirit of politics, right?
On the same level though, the Tea Party is incredibly far right socially as well. Meaning, they oppose legalization, gay marriage, Planned Parenthood ect... So, if you want to limit people from doing something, you must pass a law. To make sure the law works, it needs to be enforced... which costs money from the government. When the Tea Party talks about cutting from government, it's only the programs they oppose that are in the crosshairs.
Rand Paul was mentioned earlier in the thread. I am certainly not a Tea Party supporter, but I do like the fact that he mentioned cuts to the military along with other parts of government. He actually wants to cut everything rather than cherry pick the things he opposes. And I give him credit for that.