It’s easy enough to nationalize a congressional campaign. It’s been done before and was the reason behind the GOP success in 94. Run against the “Washington establishment” and label your ten-term congressman opponent as part of the problem, regardless of what party he is from.
Again, you are talking about an established group, "GOP success" in your earlier post you were saying "third party" and not running as a dem or rep.
As a percentage there aren't that many independents or third party members of congress.
If you have personal wealth and/or great name recognition you may succede but with out established organizational support it would be a lot more difficult.