I don't think having another party would solve the gridlock in D.C.
Technically we already have Democrats, Republicans, Independents, Libertarian Party (founded in 1971 and is available in 48 states), Green Party (founded in 1991and is available in 36 states).
There are also numerous other parties on the local and state levels who have elected members from other political parties.
The "Tea Party" has gained more influence because it aligns itself as being a part of the Republican party.
However many moderate or traditional Republicans view them as being extreme and a detriment to national elections. They tend to view compromise as weakness and aren't likely to attract Independent and conservative Democrats to vote for them.
Essentially they're only hurting their own party with stances on personal issues as well as their notion that business in Washington needs to be destroyed and rebuilt from the ground up. That rhetoric plays well for the supporters but not the masses in a general election.